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prime factorization of 624

Guest May 29, 2015

Best Answer 

 #7
avatar+26329 
+10

I was deriving thejamesmachine's method for determining if a number is divisible by 7.  Here's how he expressed it

 

For seven:

Take the last digit, double it, and subtract it from the rest of the number. If the answer is divisible by 7 (including 0), then the number is also divisible by 7:

861:86-1x2=84

84/7=12

 

.

Alan  May 30, 2015
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10+0 Answers

 #1
avatar+78755 
+5

624  =

 

312 * 2  =

 

156 * 2 * 2 =

 

78 * 2 * 2 * 2 =

 

39 * 2 * 2 * 2 * 2

 

13 * 3 * 2 * 2 * 2 * 2 =

 

2^4 * 3 * 13

 

 

CPhill  May 29, 2015
 #3
avatar+78755 
+5

Thanks, thejamesmachine for that link....I didn't know the "trick" for testing 7 as a factor.........

 

{Now....I want to see if I can figure out WHY that works.......LOL!!! )

 

 

CPhill  May 29, 2015
 #4
avatar+91053 
+5

Yes Chris, I agree, that would be a good challange  :)

 

I had not heard of it before james put it on the forum either .   Thanks James

Melody  May 30, 2015
 #5
avatar+26329 
+5

Is N exactly divisible by 7?

 

Let N = 10n + a    where n and a are integers and a is in the units position.

 

Construct M = n - 2a   (i.e. twice the units value subtracted from what's left, where what's left is considered to be a number in its own right).

 

If M is exactly divisible by 7 then we can write  n - 2a = 7m  where m is an integer.

So n = 7m + 2a

 

In that case N = 10(7m + 2a) + a  or  N = 70m + 21a

 

So N/7 = 10m + 3a and since m and a are integers the resulting value of N/7 is an integer.  i.e. N is exactly divisible by 7 with no remainder.

.

Alan  May 30, 2015
 #6
avatar+91053 
0

I have forgotten what you are proving Alan :/

Melody  May 30, 2015
 #7
avatar+26329 
+10
Best Answer

I was deriving thejamesmachine's method for determining if a number is divisible by 7.  Here's how he expressed it

 

For seven:

Take the last digit, double it, and subtract it from the rest of the number. If the answer is divisible by 7 (including 0), then the number is also divisible by 7:

861:86-1x2=84

84/7=12

 

.

Alan  May 30, 2015
 #8
avatar+91053 
0

Thanks Alan :)

Melody  May 30, 2015
 #9
avatar+78755 
0

Thanks for that proof, Alan.....

 

CPhill  May 30, 2015
 #10
avatar+631 
+8

Welcome for the method!

thejamesmachine  May 30, 2015

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