Question

If n is any positive 2-digit integer, what is the greatest positive integer that must be a factor of n(n+1)(n+2)(n+3)?

Answer 1

Explanation:

Notice that in n(n + 1)(n + 2)(n + 3):

Exactly 2 of them are multiples of 2,

At least 1 of them is a multiple of 3, and

At least 1 of them is a multiple of 4.

Since one of the multiples of 2 is already counted in the multiple of 4 we can ignore it.

Hence we have 2 * 3 * 4 = 24.

The greater positive integer that must be a factor is 24.