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What is the greatest value of m such that 4^m is a factor of

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Joined: 14 Oct 2015
Posts: 1648

Kudos [?]: 839 [0], given: 2

Location: United States (CA)
Re: What is the greatest value of m such that 4^m is a factor of [#permalink]

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24 Aug 2017, 16:13
rxs0005 wrote:
What is the greatest value of m such that 4^m is a factor of 30! ?

(A) 13
(B) 12
(C) 11
(D) 7
(E) 6

Since 4 = 2^2, we are actually trying to determine the greatest value of m such that 2^2m is a factor 30!.

Let’s determine the number of factors of 2 within 30!. To do that, we can use the following shortcut in which we divide 30 by 2, and then divide that quotient by 2 again, continuing this process until we no longer get a nonzero integer as the quotient.

30/2 = 15

15/2 = 7 (we can ignore the remainder)

7/2 = 3 (we can ignore the remainder)

3/2 = 1 (we can ignore the remainder)

Since 1/2 does not produce a nonzero quotient, we can stop.

The next step is to add up our quotients; that sum represents the number of factors of 2 within 30!.

Thus, there are 15 + 7 + 3 + 1 = 26 factors of 2 within 30!, and thus 26/2 = 13 factors of 4 within 30!.

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Kudos [?]: 839 [0], given: 2

Re: What is the greatest value of m such that 4^m is a factor of   [#permalink] 24 Aug 2017, 16:13

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