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# What is the greatest integer, k, such that 5^k is a factor of the prod

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Math Expert
Joined: 02 Sep 2009
Posts: 58428
What is the greatest integer, k, such that 5^k is a factor of the prod  [#permalink]

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24 Jan 2019, 03:29
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Difficulty:

15% (low)

Question Stats:

72% (00:51) correct 28% (01:02) wrong based on 48 sessions

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What is the greatest integer, k, such that 5^k is a factor of the product of the integers from 1 through 24, inclusive?

A 1
B 2
C 3
D 4
E 5

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Concentration: Accounting, Finance
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Re: What is the greatest integer, k, such that 5^k is a factor of the prod  [#permalink]

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24 Jan 2019, 03:45
Bunuel wrote:
What is the greatest integer, k, such that 5^k is a factor of the product of the integers from 1 through 24, inclusive?

A 1
B 2
C 3
D 4
E 5

product of the integers from 1 to 24 = 24!

5^k is a factor of 24!.

greatest value of k.

24/5 = 4.

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Re: What is the greatest integer, k, such that 5^k is a factor of the prod  [#permalink]

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24 Jan 2019, 04:44
Bunuel wrote:
What is the greatest integer, k, such that 5^k is a factor of the product of the integers from 1 through 24, inclusive?

A 1
B 2
C 3
D 4
E 5

to determine the 5^k factor ; value of k
24!/5 = 4

IMO D
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Posts: 3078
Re: What is the greatest integer, k, such that 5^k is a factor of the prod  [#permalink]

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24 Jan 2019, 04:58

Solution

Given:
• $$5^k$$ is a factor of the product of the integers from 1 through 24, inclusive

To find:
• The greatest integer value of k

Approach and Working:
• k = the number of 5’s in 24!
• Implies, k = $$[\frac{24}{5}] + [\frac{24}{25}] = 4 + 0 = 4$$

Therefore, the maximum possible value of k = 4

Hence, the correct answer is Option D

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Re: What is the greatest integer, k, such that 5^k is a factor of the prod   [#permalink] 24 Jan 2019, 04:58
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