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Problem solving

by danjuma » Tue Nov 23, 2010 4:11 pm
n is a positive integer and k is the product of all integers from 1 to n. If k is a multiple of 1440, then the smallest value of n is?

a. 2

b.4

c. 12

d.8

e.30.
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by goyalsau » Tue Nov 23, 2010 7:35 pm
danjuma wrote:n is a positive integer and k is the product of all integers from 1 to n. If k is a multiple of 1440, then the smallest value of n is?

a. 2

b.4

c. 12

d.8

e.30.
!6 = 720
!7 = 5040 ( which is not a multiple of 1440 )
!8 = 40320

1440 * 28 = 40320,

So answer must be D 8
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by Rahul@gurome » Tue Nov 23, 2010 7:37 pm
Solution:
k = n!.
1440 = 2^5 * 3^2 * 5.
Since 1440 is dividing n!, n has to be more than or equal to 5.
Check the options for n more than 5.
8 is one. 8! = 2^(7) * 3^(3) * 5 * 7.
Obviously 1440 is dividing 8!.
So d. which is 8 is the correct answer.
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