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The greatest common factor of two numbers is 5!. Which of the followin

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The greatest common factor of two numbers is 5!. Which of the followin  [#permalink]

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New post 26 Jan 2015, 05:57
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A
B
C
D
E

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Re: The greatest common factor of two numbers is 5!. Which of the followin  [#permalink]

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New post 02 Feb 2015, 04:59
Bunuel wrote:
The greatest common factor of two numbers is 5!. Which of the following can be the second number, if one of the numbers is 8!?

A. 3(5!)
B. 4(5!)
C. 5(5!)
D. 6(5!)
E. 7(5!)

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

Remember that the Greatest Common Factor of two numbers represents the overlap of all prime factors of those two numbers. So what you're looking for in this case is a value that does not share any other prime factors with 8 * 7 * 6 * 5 * 4 * 3 * 2 other than 5 * 4 * 3 * 2.

Consequentially, the answer choice cannot include any prime factors of 8, 7, or 6 outside of the parentheses, where the common 5! already exists. A is incorrect because 3 is a factor of 6. B is incorrect because 4 is a factor of 8. D is incorrect because of the common 6 and E is incorrect because of the common 7. With choice C, however, there's no overlap in factors between 5 and the set 8, 7, 6, so that means that the Greatest Common Factor is, indeed, 5!.
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Re: The greatest common factor of two numbers is 5!. Which of the followin  [#permalink]

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New post 26 Jan 2015, 07:29
ans is C..
8! can be written as 5!*6*7*8 so other given choices will increase the common factor and 5!*5 will keep GCF as 5!
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Re: The greatest common factor of two numbers is 5!. Which of the followin  [#permalink]

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New post 26 Jan 2015, 14:15
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GCF is the product of common factors of the numbers involved.

GCF = 5!

a = 8! = 8*7*6*5!

b will certainly have 5! and cannot have any more common factors with a (as this will increase the GCF)

Looking at the answers only 5 (5!) and 8! will have GCF as 5!

Ans C
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Re: The greatest common factor of two numbers is 5!. Which of the followin  [#permalink]

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New post 27 Jan 2015, 11:44
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It is given that GCD of two numbers is 5! => this is the maximum common factor in those two numbers.

First number is 8! = 8*7*6*5!
Lets review all the options for second number -

A. 3(5!) - here 3 is also common in addition to 5!. Hence 5! cant be the GCD of these two numbers
B. 4(5!) - Here 4 is common besides 5! and so this option is rejected
C. 5(5!) - only 5! is common in the two numbers and hence the Answer.
D. 6(5!) - 6 is common besides 5! and hence rejected on similar grounds
E. 7(5!) - 7 is common besides 5! and so this is aso rejected

Hence ans is C.
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Re: The greatest common factor of two numbers is 5!. Which of the followin  [#permalink]

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New post 11 Apr 2019, 23:04
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Re: The greatest common factor of two numbers is 5!. Which of the followin   [#permalink] 11 Apr 2019, 23:04
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