Is Integer Factorization Harder Than RSA Factorization?

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

• Answer:

  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.