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# What is the greatest value of integer n such that 5^n is a factor of

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Math Expert
Joined: 02 Sep 2009
Posts: 59722
What is the greatest value of integer n such that 5^n is a factor of  [#permalink]

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02 Dec 2016, 06:58
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What is the greatest value of integer n such that 5^n is a factor of 15! ?

A. 1
B. 2
C. 3
D. 4
E. 5

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Joined: 02 Nov 2013
Posts: 67
Location: India
Re: What is the greatest value of integer n such that 5^n is a factor of  [#permalink]

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02 Dec 2016, 08:07
From 15! values which will have value 5 in numbers are 15, 10 and 5.
15 will have one 5, 10 will have one 5 and 5 itself.

Hence, greatest value of integer n such that 5^n is a factor of 15! = 3. I hope that is the answer.
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Joined: 12 Sep 2015
Posts: 4145
Re: What is the greatest value of integer n such that 5^n is a factor of  [#permalink]

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22 Nov 2019, 17:06
Top Contributor
Bunuel wrote:
What is the greatest value of integer n such that 5^n is a factor of 15! ?

A. 1
B. 2
C. 3
D. 4
E. 5

-----ASIDE---------------------
A lot of integer property questions can be solved using prime factorization.
For questions involving divisibility, divisors, factors and multiples, we can say:

If k is a factor of N, then k is "hiding" within the prime factorization of N

Consider these examples:
3 is a factor of 24, because 24 = (2)(2)(2)(3), and we can clearly see the 3 hiding in the prime factorization.
Likewise, 5 is a factor of 70 because 70 = (2)(5)(7)
And 8 is a factor of 112 because 112 = (2)(2)(2)(2)(7)
And 15 is a factor of 630 because 630 = (2)(3)(3)(5)(7)
-----BACK TO THE QUESTION!---------------------

What is the greatest value of integer n such that 5^n is a factor of 15! ?
In other words, "How many 5's are hiding within the prime factorization of 15!"
15! = (15)(14)(13)(12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)
= (3)(5)(14)(13)(12)(11)(2)(5)(9)(8)(7)(6)(5)(4)(3)(2)(1)
There are three 5's in the prime factorization of 15!
In other words, 5³ is a factor of 15!

Cheers,
Brent
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Re: What is the greatest value of integer n such that 5^n is a factor of  [#permalink]

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27 Nov 2019, 12:12
Bunuel wrote:
What is the greatest value of integer n such that 5^n is a factor of 15! ?

A. 1
B. 2
C. 3
D. 4
E. 5

Since 15! has 3 prime factors of 5 (1 prime factor of 5 from each of the numbers 5, 10 and 15), the greatest value of n is 3.

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Re: What is the greatest value of integer n such that 5^n is a factor of   [#permalink] 27 Nov 2019, 12:12
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# What is the greatest value of integer n such that 5^n is a factor of

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