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smallest possible value

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by uptowngirl92 » Mon Sep 28, 2009 6:49 pm
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
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by sunnyjohn » Mon Sep 28, 2009 6:59 pm
k = n! = 1440x

n! = 720*2*x
n! = 6! *2*x

we have to make it a factorial, smallest possible:

next possible factorial is 7 :- x ==> 3.5 (hmm i m assuming that x is positive integer)

next possible factorial is 8 :- x ==> 28
put x = 28
n! = 6!*2*28 ==> 6!*7*8
n!= 8!

n = 8 :---> least possible value of n is 8.
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by okigbo » Wed Oct 21, 2009 11:52 am
Is there another explaination of how to solve this problem?
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