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What is the greatest value y for which 4^y is a factor of 12!?

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Re: What is the greatest value y for which 4^y is a factor of 12!?

by Brent@GMATPrepNow » Sun Feb 16, 2020 6:48 am
BTGmoderatorDC wrote: ↑
Fri Feb 14, 2020 4:03 pm
 What is the greatest value y for which 4^y is a factor of 12!?

A. 2
B. 3
C. 4
D. 5
E. 6

12! = (12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)
= (2)(2)(3)(11)(2)(5)(9)(2)(2)(2)(7)(2)(3)(5)(2)(2)(3)(2)(1)
= (2^10)(3)(11)(5)(9)(7)(3)(5)(3)(1)
= (2^2)^5(3)(11)(5)(9)(7)(3)(5)(3)(1)
= (4)^5(3)(11)(5)(9)(7)(3)(5)(3)(1)

So, 4⁵ is a factor of 12!, which means the correct answer is D

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: What is the greatest value y for which 4^y is a factor of 12!?

by swerve » Sun Feb 16, 2020 1:10 pm
BTGmoderatorDC wrote: ↑
Fri Feb 14, 2020 4:03 pm
 What is the greatest value y for which 4^y is a factor of 12!?

A. 2
B. 3
C. 4
D. 5
E. 6


OA D

Source: Veritas Prep
\(4^5\) is the biggest factor in terms of \(4^y\) of \(12!\).

Therefore, \(y\)'s maximum value can be \(5\).
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