Find the smallest positive integer n such that n has exactly 144 distinct positive divisors and there are 10 consecutive integers among them (Note: 1 and n are both divisors of n)

110880 = 2^5 * 3^2 * 5^1 * 7^1 * 11^1

and 6 * 3 * 2 * 2 * 2 = 144.

You need to have a core of 2^3*3^2*5*7 = 2520 because in any set of 10 consecutive integers, you will have a multiple of each of 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.  Then find the smallest number to multiply by 2520 that will satisfy the 144 divisor requirement (44).

Posted by Chelsea on 2006-02-20 16:29:58