Prime factorization problem

suppose n is a positive integer with the following properties:
n/24 is divisible by 10 but not 20
n/15 is divisible by 6 but not 18
n is not divisible by 35, 100, or any prime number with 2 or more digits

what is the prime factorization of n? please show how you get the answer! thanks in advance

First constraint tells us that n has factors 2,2,2,3 (since n/24 is an integer), as well as 2,5 but no more 2's.

Second constraint tells us that n has factors 3,5 as well as 2,3 but no more 3's

So far we have n = 2x2x2x2x3x3x5 = 720, and no more 2's or 3's. The third constraint is met already, so we simply have n=720.