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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)
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
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.
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