n is a positive integer, and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1440, then the smallest possible value of n is?
A. 8 B.12 C.16 D.18 E.24
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Re: A Question about Interger
n is a positive integer, and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1440, then the smallest possible value of n is?
A. 8 B.12 C.16 D.18 E.24
If K is a multiple of 1440 then minimum prime factors of k = 2^5 * 3^2 * 5^1
Also,
k is the product of all integers from 1 to n inclusive = n!
If we take n = 8 => 8! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 = 2^7 * 3^2 * 5^1 * 7^1 = this contans all the above factors
So answer is 8 (a)
A. 8 B.12 C.16 D.18 E.24
If K is a multiple of 1440 then minimum prime factors of k = 2^5 * 3^2 * 5^1
Also,
k is the product of all integers from 1 to n inclusive = n!
If we take n = 8 => 8! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 = 2^7 * 3^2 * 5^1 * 7^1 = this contans all the above factors
So answer is 8 (a)
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