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1)What is the least positive multiple of 72 that has exactly 16 positive factors?

 

2)The product of the proper positive integer factors of n can be written as n^(ax+b)/c , where x is the number of positive divisors n has, c is a positive integer, and the greatest common factor of the three integers a, b, and c is 1. What is a+b+c?

 

3)If m is a 3-digit positive integer such that lcm[8m,10^10] = 4*lcm[m,10^10], then what is the value of m?

ReallyBadAtMath  Aug 15, 2018
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1)What is the least positive multiple of 72 that has exactly 16 positive factors?

 

The least positive multiple of 72 that has exactly 16 positive factors is: 23,328 = 2^5 * 3^6

72 x 23,328 =1,679,616=2^8 x 3^8 =16 prime factors.

Guest Aug 15, 2018
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Mr. BB,  you are confusing prime factors with factors. There are at least two other questions where you have conflated the two. They are not the same thing. I corrected your screw ups, but I didn’t troll you for it, so we’re dealing with it again.

 

Write this down on a sticky-note and stick it on your computer screen.  Prime factors and factors (divisors) are NOT the same thing!

 

GA

GingerAle  Aug 15, 2018
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Who are you lecturing as "Mr. BB", you monkey face? How do know what the questioner meant?

I  read factors to mean "prime factors" and, accordingly, provided the answer. If you disagree, then all you do is provide the questioner with your interpretation and give YOUR answer accordingly. let him/her choose between the two. Don't pontificate on anything or everything, because nobody gives a rat's behind of what you think. Go climb a tree!!. 

Guest Aug 15, 2018
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Who are you lecturing as "Mr. BB", you monkey face? How do know what the questioner meant?

 

I’m lecturing Mr. BB(4) --the Bullshit Bug, a genetic variant of the dung beetle that, instead of rolling dung into a ball, it spreads it allover the forum. This is an accurate description of what you usually do.

(Related comments)   

 

How do know what the questioner meant?

I’m a genetically enhanced chimp with advanced mind-reading skills.

 

I read factors to mean "prime factors" and, accordingly, provided the answer.

 

Well, along with needing improvement in your reading skills, you need improvement in your math skills: your prime factor answer is wrong.

 

If you disagree, then all you do is provide the questioner with your interpretation and give YOUR answer accordingly. let him/her choose between the two.

 

Math by consensus. Let’s see how that might work: 1+1=2 if and only if the majority agree. Well, it works for this question most of the time. You should abstain from the voting though. You also should abstain from posting math solutions. You should write that on a sticky-note.

 

Don't pontificate on anything or everything, because nobody gives a rat's behind of what you think. Go climb a tree!!. 

 

That’s not true. Many care what about what I write and, by extension, what I think. Melody welcomed me back after a brief absence. I’m sure others care too. As for general readers, I’ve pointed out the view counts before. In this case, with a measly 14 views, the count will move to 29 or more --that is at least 15 more unique views by this time tomorrow. I’m sure this irritates you, but many like to read comments from a genetically enhanced chimp, and not very many care to read comments from a mutant dung beetle, commonly known as a bullshit bug.   

 

Now, I will go climb a tree because I have a nice tree house there.

 

GA

GingerAle  Aug 16, 2018
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Yep, I care about what Ginger writes and thinks. I wanted her to come back sooner.

https://web2.0calc.com/questions/help-asap-please_14#r1 I got 2 negs for my post. I don’t know if that was for calling the answer BS or for wanting her to come back.

JacobBernoulli  Aug 16, 2018
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Maybe it was one neg for each comment.smiley

GingerAle  Aug 16, 2018
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"Your prime factor answer is wrong." Why in the h**l don't you post your own "correct" answer and shut up??!! You "genetically enhanced chimp" should stick to your monkey business! Quite clearly, this is out of your league! I looked briefly at your profile. What the h**l do you think makes you an "expert" in math? I clearly see that you are seeking a confrontation with anybody and everybody. What the h**l is the matter with you? Are you a "normal" being or do have "mental problems"? If the latter, then seek professional help. I suggest that if you wish to reform the world, then start with yourself!!. God knows you needed it badly!.
Divisors of 60 =1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Prime "factors" of 60 = 2^2×3×5 (4 prime factors, 3 distinct)
Do you see the difference?? A "divisor" such as 12, or 30 above may have MANY prime "factors". But a "factor", such as 2, 3, 5 above NEVER has a "divisor"!! YOU confuse the two, you "Genetically Enhanced Chimp"!.

Guest Aug 16, 2018
 #6
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The least multiple of 72 that has exactly 16 prime factors is 72*211, not 72*25*36

 

EDIT: my bad, its 211, not 213

Guest Aug 16, 2018
edited by Guest  Aug 16, 2018
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This forum has many “mathematicians” who could answer this question, but we need a Master Troll to keep the forum’s troll bridge’s structure from deteriorating, and, not to forget, the sewer system free-flowing.

JacobBernoulli  Aug 16, 2018
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Why in the h**l don't you post your own "correct" answer and shut up??!!

It’s much more beneficial (not forgetting enjoyable) for the forum to give you heII for your, now confirmed, BatShit stupidity, than it is to give a one-off answer to a basic high school (Jr. high) question--that I’ve answered at least once before. You know… give someone a fish and you feed him for a day, stop someone from grazing on BS and you keep him from getting sick. Unless that someone is a dung beetle larva, then it’s nutritious--which is probably why you are full of it.  

 

What the h**l do you think makes you an "expert" in math?

 

I don’t think any such thing. It just seems that way to you because you are so poor in the subject. You really can’t see things you don’t understand. Some will latch on to ideas they do understand and erroneously apply them. From this, all sorts of convoluted illogicality arises, and it becomes a way of life.  You understand BS, so that is what you apply, and the way of your life is that of a bullshit bug.

 

Confirmation of BatShit stupidity:

 

Divisors of 60 =1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Prime "factors" of 60 = 2^2×3×5 (4 prime factors, 3 distinct)
Do you see the difference?? A "divisor" such as 12, or 30 above may have MANY prime "factors". But a "factor", such as 2, 3, 5 above NEVER has a "divisor"!!

 

I need a babble translator to figure out most of what you wrote.  Though I now understand how you arrived at such an absurd solution. Yep, you should definitely abstain from any and all “math by consensus” votes. 

 

GA

GingerAle  Aug 16, 2018
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Ginger speaks: Yep I screwed up. I neglected the caveat of “at least” in the question.

Ginger Troll speaks: I didn’t post a wrong answer. I correctly answered the wrong question. A home run on an error is still a home run. laugh

GA

GingerAle  Jul 19, 2018
https://web2.0calc.com/questions/help-please_81710#r4

Guest Aug 16, 2018
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I remember that post, I was the one who commented on it. Ginger’s twin responses were because of my comments. Though I suppose she might have made similar comments anyway.

 

 “A home run on an error is still a home run.” LMAO! This is truly a great retort.

 

What’s your point? What does this have to do with anything here?

JacobBernoulli  Aug 16, 2018
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Ginger, i have to agree with the guest- you are very quick to judge others, and a large portion of your posts is dedicated to bashing other users, some with wrong answers and some with perfectly fine answers. There is no need to attack other users for their answers when their mistakes can be explained to them calmly, but it seems that you just want to cuss them out and to ridicule them.

 

We all make mistakes, including you, and it's very hypocritical for you to attack others for getting math problems wrong when your posts show that you make mistakes too. The guest gave a good example.

 

The guest in this thread was wrong- he got the question wrong and gave a wrong solution to the question he thought RBAM was referring to, but there is no need to verbally attack him for that. Keep in mind that many users here are high school students- they're here to learn, and cussing them isn't going to help anyone, its just going to lower their self esteem, and bashing students in the head for failing a challenge or slipping up is not going to encourage them to keep learning.

 

please take this into consideration

Guest Aug 16, 2018
edited by Guest  Aug 16, 2018
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Well look who joined the parade …the one and only Blarney Master. Longtime no see. (Not long enough, though.)

----

please take this into consideration

Why of course, that’s a very reasonable thing to ask.

 

We all make mistakes, including you, and it's very hypocritical for you to attack others for getting math problems wrong when your posts show that you make mistakes too.

Why, far be it from me to be a hypocrite. And of course I’ll excuse the decomposing rat in your kitchen, because well, all kitchens have germs--even mine. You’ll understand if I don’t indulge. We chimps enjoy tasty rats and voles, but I prefer mine on the fresh side. Though, if I turn in to Chimp Hyde, I might.

 

Keep in mind that many users here are high school students- they're here to learn, and cussing them isn't going to help anyone

The only high school student I’ve (knowingly) trolled is Max Wong. It wasn’t for his math (the kid is brilliant), it was for juvenile rudeness. My troll post was more rude than he was. Alan hid it, as I was editing it. Max never saw it.    

 

Ginger, i have to agree with the guest- you are very quick to judge others,

So a “guest” quotes a my post, where I admit a mistake, and you agree with the guest that I’m very quick to judge others.  That’s not a stretch, it’s a complete non sequitur. You should have used this post, where I admit to exactly what you say. But what the heII, whether it’s math or character analysis, any blarney and bullshit will will suffice. Right?

 

and a large portion of your posts is dedicated to bashing other users,

Humph… that’s not the half of it: Some of my best work is hidden from public view.  

 

some with wrong answers and some with perfectly fine answers.

Only you and your idiot BB brothers would think the answers are perfectly fine.  

 

There is no need to attack other users for their answers when their mistakes can be explained to them calmly, but it seems that you just want to cuss them out and to ridicule them.

The heII, you say! If I trolled answerers for their mistakes, I won’t have time to do anything else. I primarily troll idiots and *morons who perpetually present errant math with varying degrees of erudition. There are only a hand-full of them on here, but they present more than two-thirds of the BS. Most are in the “BB” class: “Blarney Banker,” the “Blarney Bag,” the “Bubble Brain,” and “*Bullshit Bug,” aka “Mr. Pipsqueak,” These all profile as post retirement-age males --oh, and of course, as idiots. Then there’s (you) the “Blarney Master,” who is college-age. There are a few others who’ve made a few posts, but they didn’t stick around--perhaps because my trolling chased them off. If so, that’s great. It’s lightens the load on the forum’s sewer system.  

 

These idiots, all have common factors (that’s all factors, not just prime factors). The obvious common factor is they post as anonymous guests. Some have accounts, but but they don’t use them for posting. Now, why might that be? The obvious answer is they don’t want an index for their BS mathematics. Every post is new, and there is no responsibility or accounting for the yesterdays. They don’t want to risk having to account for the massive, repetitious piles of slop and errant math. Having to account for the real-world, in the real-world, disrupts the fantasy world.   

 

Another common factor is in the defence of their posts; it’s rarely with mathematics, and it usually includes a variation of “Well, this is the way I do it,” or, “This is the way I interpret it,” Mr. Pipsqueak actually supported his point with a mathematical statement. This, I will say, makes it very clear that convoluted errant mathematical logic can exist in space time long enough to distort realistic perception. Other defence statements include “You are out of your league,” “Go back to school and learn some math,” etc, etc, etc …   

 

Yet another common factor, this one based in the motivation for this perpetual regurgitation of preposterous postulates of mathematics. The motivation seems to be based in romance fantasy going back to childhood. The self-narrative may follow something like this:

 

“Well, I’m retired from my truck-driving and ditch-digging jobs, let’s see, I wanted to be a scientist when I was a kid, and I would have been too, if I had actually studied, but …well I have the time to study now. Scientists need to know math; yeah, I’ll start with that. I was good at math when I was in school…I had the multiplication tables down pat by 10th grade, before I dropped out…or was I expelled? I can’t remember. Anyway, it helped that I had to repeat forth-grade, so I’m half way there. It shouldn’t take me more than two months to get-up-to-speed; three, at the most. Yep, that’s what I’ll do. …”

 

The reality of this is out of reach, but the fantasy isn’t. This wouldn’t matter if it remained in their world, but it’s presented in this world where it doesn’t work. Hapless bystanders are drawn into this mush. It’s not criminal, but it needs a warning sign: Fallacious Math and Malicious Logic ahead. Proceed with caution! 

 

There is no need to attack other users for their answers when their mistakes can be explained to them calmly, but it seems that you just want to cuss them out and to ridicule them.

I don’t curse that much, you fucking idiot! I explain the mistakes to the dumb aholes in a very calm and collected troll manner. They’re the ones who rant and rave. No one likes to be trolled for their stupidity, no matter how much they deserve it.   What the heII is a matter with you?

 

With that, I’ll sign off. (Before this post becomes truly blank worthy.)indecision

 

 

GA

GingerAle  Aug 17, 2018
edited by GingerAle  Aug 17, 2018
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The only high school student I’ve (knowingly) trolled is Max Wong

 

Wrong. here you harass miranda after he got banned, here you scold an AoPS student and here you calmly correct a "12-year-old". It's very convenient for you to categorize everyone as a "BB", as a dumb kid or as an old, uneducated nobody. I'm not college aged nor am i a "post retirement aged male", but that is how you categorize me, making it so much easier to criticize me.

 

Funnily enough, you barely categorize any of them as high school students, so it's never your mistake if what i mentioned DOES apply to you- you just didn't know they were highschool students. my point wasn't that you knowingly troll high school students or that you take pleasure in viciously attacking poor, helpless students.

 

 

So a “guest” quotes a my post, where I admit a mistake, and you agree with the guest that I’m very quick to judge others.  That’s not a stretch, it’s a complete non sequitur.

 

"Don't pontificate on anything or everything, because nobody gives a rat's behind of what you think"

 

"I clearly see that you are seeking a confrontation with anybody and everybody"

 

 

Only you and your idiot BB brothers would think the answers are perfectly fine.

 

But you yourself admitted in various posts, including here, here and here that you did just that.

Guest Aug 17, 2018
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You are a delicate snowflake, BM. The least bit of heat melts you into mush. You’re so heart-felt concerned about the feelings of the morons who continuously post mathematical dung, or actively vandalize the forum, or waste answerers’ time with subterfuge. But you are not concerned about the members and guests who have to constantly step around or walk through the bovine fecal matter. You are unconcerned about the potential thousands of visitors who will never see the brilliant solutions by Melody, Alan, CPhil, Heureka, and Hectatar, Because Miranda destroyed the questions. You bleed and melt for the wrong people. Why do you have an affinity for wilful morons and vandals?

 

Wrong. 

His name is Wong. Making fun of a persons name is not very PC, BM!

 

here you harass miranda after he got banned,

Miranda is a “her,” and her name is spelled with an uppercase “M”

I wasn’t harassing her. I was celebrating her banishment. It’s a unique accomplishment to be publicly banished by Andre Massow. That’s not something that happens very often.

 

This brought back fond memories. I didn’t elaborate on the details in the post, but if you want to know then read on. …

As I said in the post, I was expelled from my parochial school when I was about her age, but not for vandalism though—I posted on my MySpace, a mock social news GingerAle byline, with several photos of Sister Alice “doing” Jesus. The main photo caption read “Sister Alice, Bride of Christ, consummates her marriage”

 

My eight linked friends thought the post was hilarious, so did thousands of others—the post went viral. In less than three days I had hundreds of friend requests, and several death threats too. Sister Alice didn’t think much of it, and neither did the school and church hierarchy. My post and photos were so well presented, the hierarchy, at first, actually thought Sister Alice had flipped her lid. The young children in the background of the photos added to the potential of scandal. If nothing else, my “quote” from Jesus about the “pent up *passions of older *virgins” should have been a major clue the post was opportunistic mockery.  

 

A child had used Jesus’ face for target practice for sticky Nerf darts. Sister Alice had simply shinnied up a nearly eight-foot tall wooden statue of Jesus to remove them. When she slid back down, her skirt snagged and it drew up around her butt causing her to become stuck when she was at the mid section of the statue. I had been photo-documenting the event with my nifty, new digital camera. At this point, I was certain there was a patron saint for photographers. One who has a marvellous sense of humor.

 

The best photos were of Sister Alice arching her back in an attempt to unsnag herself. It dawned on me, if that statue fell on her, it would crush her—not that this was a bad thing, but there were young children standing around watching the spectacle. I had them stand further back, to avoid injury, in case it fell. No such luck, but if it had fallen on her, her postmortem photo caption would have read: “Jesus goes down on Sister Alice, sends her into eternal rapture.”     

 

You know, BM, if you were in that judgment circle you could have advocated for me.

 

“Ginger didn’t know what she was doing. You are just being mean to her.”

Oh yes, she did know. She just didn’t know it would bounce around the world and end up on the desk of the archbishop.  

 

“You should just explain to her in a nice, calm way what her mistake was, then she won’t do it any more.”

Oh yes, she will, and she did even worse. She gave an apology gift to Sister Alice that was so blasphemous, she tried to have her excommunicated.

______

 

Anyway, back to the points at hand.  You missed this post https://web2.0calc.com/questions/cphill_13#r8

Where I blast Julius for doing the exact same thing. Melody thought I was polite; Julius, not so much. I like the little brat. He’ll make a good troll someday.

______

 

It's very convenient for you to categorize everyone as a "BB", as a dumb kid or as an old, uneducated nobody.

Of course it’s convenient to categorize. I use dumb, dumber, and dumbest because stupider and stupidest usually isn’t grammatically correct. I don’t remember using “dumb kid,” but maybe I inferred it in a counterpoint to an oldfart. It’s called regression: a return to a former or less developed state. For most of them this is a misnomer, though, because they never left the moronic state in the first place.

 

The old dog new tricks metaphor is a metaphor because it is a true-ism. If you wait until your arteries harden and your brain atrophies before you learn something, you’re not likely to live long enough to learn it. I’m sure this disturbs you, but these are facts of nature. It’s probably doubly disturbing and ironic for you, because you are just getting intelligent enough to realize that you are always going to be a moron, no matter what you do. On the bright side though, you don’t have to worry about regression.    

 

but that is how you categorize me, making it so much easier to criticize me.

Humm. You fit into many categories (of stupid). It’s always quite easy to criticize you. Here’s one: You are very skilled at writing completely non sequitur paragraphs.

 

 I'm not college aged …

OK. You do seem a little immature, I though you were a high school student, who flunked a few grades. I mis-attributed some of your writing errors, because English is a second language for you. Your syntax and structure suggests English is an educational language. You probably attend school in Holland or a former Dutch colony.

 

here you scold an AoPS student

That AoPS student is one of your creations. You’ve created puppets before, Puppetmaster/Blarneymaster.

 

A “kid” shows from nowhere, posts neurotic swill commentary around moderately sophisticated, unformatted LaTex code, to counter my post. He returns to confirm the AoPS approval of his answer, then he disappears —no more answers or questions.  Humm…  It took me a few days to realize it was you.

 

here you calmly correct a "12-year-old"

Here’s a statistical question for you.

What’s more likely:

A mother of a 12-year-old, with senior high school writing skills, who adopts the persona of her child to post a question, or a 12-year-old with senior high school writing skills, who adopts the narration view point of her mother to post a question?

 

In any case, I accepted her response and spent three hours researching the academic requirements of the school to give her an informed answer, to wit, there was no acknowledgement. A blòódy waste of time.   

 

you take pleasure in viciously attacking poor, helpless students.

No one gets a free pass on the Troll bridge, BM.

 

With that, I’ll conclude, because the rest of your post is too incoherent for a response.

 

This was great, BM; come back and visit again sometime. … or not …

 

 

GA

GingerAle  Aug 19, 2018
edited by GingerAle  Aug 19, 2018
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ROF LMFAO!! I’m going to stroke. I’ve just returned from visiting with my grandchildren, now I’m going to keel over from unrecoverable laughter.  I’ve taken a handful tranquilizers with a double scotch, so I think I can hang on until you post the pics of Sister Alice doing her thing. ROF LMFAO I’m going to stroke! ………

JacobBernoulli  Aug 23, 2018
 #14
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1)

The question clearly says "factors", not "prime factors", so let's try and answer the question. Firstly, what are the factors of 72? A factor is an integer that divides the number without leaving a remainder, so 1 and 72 are factors, as are 2,3,4,6,... and so on. In fact the prime factorization of 72 is \(2^3\times 3^2\), so you can create a factor of 72 by taking an integer power of 2 between \(2^0\) and \(2^3\)(inclusive) and multiplying it by a power of 3 between \(3^0\) and \(3^2\). Since there are 4 of the first and 3 of the second there are exactly \(4\times3=12\) factors: 1,2,3,4,6,8,9,12,18,24,36 and 72. To get multiples of 72 you can multiply by 2 to get \(2\times72=2^4\times3^2=144\) which has \(5\times3=15\) factors or 3 to get \(3\times72=2^3\times3^3=216\) has \(4\times4=16\) factors. Using larger powers of 2 or 3 or including more prime multipliers will produce way too many factors, so:

 

\(3\times72=2^3\times3^3=216\) is the least (and only) integer multiple of 72 with exactly 16 factors.

Guest Aug 17, 2018
edited by Guest  Aug 17, 2018
 #15
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What do you know, someone actually answered the original blòódy question.

GingerAle  Aug 17, 2018

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