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For what minimum value of n, the product of all positive integers from

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GMATinsight
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For what minimum value of n, the product of all positive integers from [#permalink] New post   18 Apr 2020, 07:13
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For what minimum value of n, the product of all positive integers from 1 to n is evenly divisible by 840?

A) 6
B) 7
C) 8
D) 12
E) 24

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B
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Re: For what minimum value of n, the product of all positive integers from [#permalink] New post   18 Apr 2020, 07:20
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GMATinsight wrote:
For what minimum value of n, the product of all positive integers from 1 to n is evenly divisible by 840?

A) 6
B) 7
C) 8
D) 12
E) 24


n! = 840*k, what is the minimum value of n?

\(840 = 2^3*3*5*7\)

    A) 6 - 6! does not have 7 as a factor
    B) 7 - 7! has all the required factors
Ans: B
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Re: For what minimum value of n, the product of all positive integers from [#permalink] New post   18 Apr 2020, 07:40
Let’s factorise 840. We get 840 = 2x2x2x3x4x5x7 = 2x3x4x5x7. Now we are saying that n! / 840 = k (say) ie n! = 840k = 2x3x4x5x7. If k were 6, then n! = 7!. So minimum value of n = 7. For no other value of k < 6, do we get 840k = factorial of a number. Hence answer is B.

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Re: For what minimum value of n, the product of all positive integers from [#permalink] New post   18 Apr 2020, 08:18
GMATinsight wrote:
For what minimum value of n, the product of all positive integers from 1 to n is evenly divisible by 840?

A) 6
B) 7
C) 8
D) 12
E) 24

Source: https://www.GMATinsight.com


Here the question is not saying n is inclusive in the products, hence considering it not part of the product of all positive integers from 1 to n.

Hence IMO, answer should be 8

Hence (C)
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For what minimum value of n, the product of all positive integers from [#permalink] New post   18 Apr 2020, 09:15
GMATinsight wrote:
For what minimum value of n, the product of all positive integers from 1 to n is evenly divisible by 840?

A) 6
B) 7
C) 8
D) 12
E) 24

Source: https://www.GMATinsight.com


840 factors= 2^3*3*5*7
which can be written as ; 2*4*6*5*7
so value of n has to be atleast 7 ; 7!/840 ;
OPTION B ; 7
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Re: For what minimum value of n, the product of all positive integers from [#permalink] New post   28 Mar 2024, 04:22
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