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An eight-digit integer is formed by repeating a positive four-digit integer. For example, 25,632,563 or 60,786,078 are integers of this form. What is the greatest common divisor of all eight-digit integers of this form?

 Nov 6, 2019
 #1
avatar+2490 
+1

This solution can be solved on paper if you are a higher dimensional being with amazing calculation skills. So you might need a calculator.

 

 

We find the SMALLEST of "An eight-digit integer is formed by repeating a positive four-digit integer.". The reason WHY we find the smallest is because it has the LEAST number of factors, which helps us get to the answer faster.

 

Which is 10000001

 

Looking at this, a palindromic integer (i.e. a number same backwards and forwards like 121) with an even amount of digits proves this number is divisible by 11.

 

Dividing: 10000001 / 11 = 909091

 

909091 is prime by using the prime checking method.

 

 

Now we check if anyother number can be divided by 909091.

25,632,563/909091 = 28.195816480418352

 

This means taht 909091 cannot be a factor.

 

Since 11 is the only other factor,

 

11 is the answer. (probably)

 Nov 6, 2019
edited by CalculatorUser  Nov 6, 2019
 #17
avatar+2490 
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oops i screwed up my brain is wired wrong!

 

anyways, try what I did, find the SMALLEST number that fits the problem. and prime factorize it.

CalculatorUser  Nov 6, 2019
 #2
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+1

GCD [ 60786078, 25632563, 12345123, 41879187] = 1

 Nov 6, 2019
 #15
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It appears that the right answer should be =10,001

 

gcd(60786078, 25632563, 12341234, 41874187, 52975297, 27542754, 56785678, 27512751......etc.) =10,001

 

When you factor all of them, they all seem to share the same 2 factors: 73 x 137 =10,001.

Guest Nov 6, 2019
edited by Guest  Nov 6, 2019
 #3
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Who ticked this?

 Nov 6, 2019
 #4
avatar+105971 
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The tick just means that there is an answer.

It is not an indication of correctness of that answer.

 

If the asker of the question (or anyone else i suppose) is not happy then it is up to them to say something.

The question can be unticked, if there is a polite request with a reason.

Melody  Nov 6, 2019
 #5
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Many questions have answers and are not ticked, why is that?

Guest Nov 6, 2019
 #6
avatar+105971 
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Maybe a moderator has not seen them.

Or maybe the moderator thought that the answer was very obviously inadequate.

Melody  Nov 6, 2019
 #7
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Are incorrect answers considered adequate?

Guest Nov 6, 2019
 #8
avatar+105971 
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The answers are not examined in detail, there is not enough time to examine every question.

 

It is up to members and guests to indicate, politely and with a reason, why the answer is inadequate or incorrect.

 

I have no problem with some answers being wrong. The asker should have enough knowledge to pick up careless mistakes and to question illogical answers.

If they do not understand they should ask questions and interact with the answerers.

Being ticked off does not prevent further posts on the thread.

 

If they copy the answer down without understanding, and hand it in as homework then it is good that it is wrong.  They should not be copying other people's answers anyway.

Melody  Nov 6, 2019
 #9
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Do yoy think it's a good idea to give some askers wrong answers deliberately?

Guest Nov 6, 2019
 #10
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No, I would not go that far.

But it is still up to the asker to decide whether or not to accept an answer.

 

The asker can also interact with the answerer and if they are not happy they can even request a specific answerer to intervene.

This is easier for members, they can do it by private message if they want.

They may not get the help from the specific person that they want but often they do.

 

Are you the person who asked this question?

If you are then why are you not drawing attention to your specific concerns.

and

If you are not then that is a part of my point. Questions are dumped here. Even the asker usually does not care if it is answered or if it is right and they are very often not interested in learning anything from the answer. If they want to learn, and they do not understand,  then they will interact with the answerers.  Errors will be corrected or at least identified.

Melody  Nov 6, 2019
 #11
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Maybe the question asker solved the question using a credible source? Maybe he already solved the question himself?

Guest Nov 6, 2019
 #12
avatar+105971 
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Maybe so, hence he/she is not interested in what is presented here.

People can give wonderful answers and many/most askers do not even have the good grace to say thankyou.

Maybe they have not even seen the answer. The assignment was due an hour ago, they no longer have any interest.

Melody  Nov 6, 2019
 #13
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What do you think about the answerers who don't bother to check their answers or read the question correctly? Don't you think that it can be irresponsible towards the users that come here to learn? Especially when this site hosts many knowledgeable mathematicians and has earned a grear reputation?

Guest Nov 6, 2019
 #14
avatar+105971 
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I think I have already told you what I think.

If askers want to question an answer they are encouraged to do so.

Melody  Nov 6, 2019
 #16
avatar+1814 
+3

WTF! This looks like a bloody inquisition. 

 

You plop in here as an imperious, fucking know-it-all –and you are anonymous because ...well the AssHoleMan doesn’t want to present any kind of identity. But of course, we know who you are by your erudite syntax and presentation of pure condescending BULLSHIT!

 

(Ahem) What do you think about the answerers who don't bother to check their answers or read the question correctly? Don't you think that it can be irresponsible towards the users that come here to learn?

This line is particularly condescending:

Especially when this site hosts many knowledgeable mathematicians and has earned a grear reputation?

You can take your patronizing superiority and shove it up your ass!

 

If you were truly knowledgeable about this site, you’d know there are very few knowledgeable mathematicians on this forum.  To you, anyone who knows the multiplication tables is a knowledgeable mathematician, so it’s just a matter of perspective. In any case, you are not qualified to make the statement. 

 

I’ve seen your work on here, and it’s clear you are a fucking idiot. You think of yourself as a knowledgeable mathematician and educator because you’ve provided solutions to a few junior high school math questions. I’m sure you’ll start having wet dreams when you remember how to solve quadric equations. I am personally overwhelmed by your majestic presence. You belong in the forums “BB” class. BB stands for Blarney Bag and it includes Bullshit Bugs and Blarney Bankers.  This is the league of Extraordinary Batshit Stupid Gentlemen: those who’ve retired with a pension, hardened arteries, atrophied brains, and an extreme desire prove their virile intellect via mathematics.

 

I’m sure you belong in this class. Let me guess, you are a recently retired what ... a salesman ...insurance maybe.  Whatever... You’ve not practiced any math for forty years or more, and now that you have time, and are bored-out-of-your-gourd, you’ve decided you want to help the children of the current generation.

 

How fucking noble! We are soooo honored to have you. To prove it, we will shit marble every time you post.

 

 

GA

GingerAle  Nov 6, 2019
edited by GingerAle  Nov 6, 2019
edited by GingerAle  Nov 6, 2019
 #18
avatar+667 
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what just happened....

Nirvana  Nov 8, 2019
edited by Nirvana  Nov 8, 2019
 #19
avatar+89 
+1

Ginger, you never disappoint!

You are a Troll with tremendous talents in mathematics and proctology. After reaming out the asshoIes, you burn them a new one.

ROFLAMO!  I’m going to stroke!

JacobBernoulli  Nov 10, 2019
edited by JacobBernoulli  Nov 10, 2019

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