Math Is Fun Forum

aluka

Guest

Prime Factorization

Help... can someone please explain how to get this answer (or at least rule out the others)...

The greatest common factor of n and 540 is 36.  Which of the following could be the prime factorization of n?

A.  2x3 squared
B.  2 squared x 3 to the third
C.  2 to the fourth x 3 squared x 7
D.  2 to the fourth x 3 to the fifth x 5

(the answer is C)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Prime Factorization

Hi aluka;

If you have been taught how to get the GCD using Euclids algorithm then:

http://www.mathsisfun.com/greatest-common-factor.html
http://www.math-help-ace.com/Greatest-C … actor.html

Or you can do it by inspection: 540 = 2^2 * 3^3 * 5

A is out: the GCD(2*3^2 , 2^2 * 3^3 * 5) = 2*3^2 = 18

B is out: the GCD(2^2 * 3^3 , 2^2 * 3^3 * 5) = 2^2 * 3^3 = 108

C is okay: the GCD(2^4 * 3^2 * 7, 2^2 * 3^3 * 5) = 2^2 * 3^2 = 36

D is out: the GCD(2^4 * 3^5 * 5, 2^2 * 3^3 * 5) = 2^2 * 3^3 *5 = 540

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

soroban

Member

Registered: 2007-03-09

Posts: 452

Re: Prime Factorization

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