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

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

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New post 24 Jan 2019, 03:29
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A
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C
D
E

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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
Spoiler: OA

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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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New post 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.

D is the correct answer.

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

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New post 24 Jan 2019, 04:58
1

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

Answer: 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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