Question

find the smallest possible integer value of n for which 99n is a multiple of 24.

Answer 1

For a number to be a multiple of 24, it must contain all the factors of 24; which are 2 x 2 x 2 x 3.

If you break down 99 into prime factors, it is 3 x 3 x 11.

So of (2,2,2,3), 99 contains the 3 but does not have any of the 2s.

So the smallest number would be 3 x 3 x 11 x (2 x 2 x 2) = 792 and n = 8.

Answer 2

another approach:
99n/24 = (99/24 )*n = (4 + 1/8)*n
it is obvious now that it is 8.

Answer 3

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