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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7465
GMAT 1: 760 Q51 V42 GPA: 3.82
n is a product of 6 distinct prime numbers. m!/n is an integer.  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 70% (01:03) correct 30% (01:38) wrong based on 83 sessions

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[Math Revolution GMAT math practice question]

$$n$$ is a product of $$6$$ distinct prime numbers. $$\frac{m!}{n}$$ is an integer.
What is the smallest possible value of $$m$$?

$$A. 10$$
$$B. 11$$
$$C. 12$$
$$D. 13$$
$$E. 14$$

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Re: n is a product of 6 distinct prime numbers. m!/n is an integer.  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

$$n$$ is a product of $$6$$ distinct prime numbers. $$\frac{m!}{n}$$ is an integer.
What is the smallest possible value of $$m$$?

$$A. 10$$
$$B. 11$$
$$C. 12$$
$$D. 13$$
$$E. 14$$

n = 2* 3*5*7*11*13
so m!/n can be an integer only when m = 13 !
IMO D
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Re: n is a product of 6 distinct prime numbers. m!/n is an integer.  [#permalink]

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n is a product of 6 distinct prime numbers. m!/n is an integer.
What is the smallest possible value of m?

Smallest 6 prime numbers = 2,3,5,7,11,,13
So m! should include all of them
implies smallest possible value of m = 13

Option D is correct
Manager  B
Joined: 18 Oct 2018
Posts: 83
Location: India
GPA: 4
Re: n is a product of 6 distinct prime numbers. m!/n is an integer.  [#permalink]

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m!/n is an integer.
For the value of n to be minimum, m!/n should be minimum.
But since n is a product of 6 distinct prime no.'s, the minimum value of n=2*3*5*7*11*13
So, the minimum value of m such that m!/n is an integer is 13
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7465
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: n is a product of 6 distinct prime numbers. m!/n is an integer.  [#permalink]

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=>

The smallest product of $$6$$ distinct prime numbers is $$n = 2*3*5*7*11*13.$$ $$13!$$ Is the smallest factorial that is divisible by $$2*3*5*7*11*13$$. Thus, the smallest possible integer value of $$m$$ is $$13$$.

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Re: n is a product of 6 distinct prime numbers. m!/n is an integer.  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

$$n$$ is a product of $$6$$ distinct prime numbers. $$\frac{m!}{n}$$ is an integer.
What is the smallest possible value of $$m$$?

$$A. 10$$
$$B. 11$$
$$C. 12$$
$$D. 13$$
$$E. 14$$

The smallest product of 6 distinct prime numbers is:

2 x 3 x 5 x 7 x 11 x 13, so we see that m! must have a prime of 13, so the least value of m is 13.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: n is a product of 6 distinct prime numbers. m!/n is an integer.   [#permalink] 14 Jan 2019, 19:03
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