Integer numbers are made up of factors, which are the smallest numbers that when multiplied together form the original number. Factors are always prime. 1 and the original number itself don’t count as factors. If a number has no factors, then that number is itself prime. For example, 12 is made up of three factors: 2×2×3 (even though 4×3 is 12, 4 itself has two factors: 2×2).
We care about this because factors are often involved in cryptography:
When the numbers are very large, no efficient integer factorization algorithm is publicly known; a recent effort which factored a 200-digit number (RSA-200) took eighteen months and used over half a century of computer time.
Though we’ll be dealing with much smaller numbers for now.
The input file DATA2.txt will contain 5 lines, integers 2 ≤ N ≤ 32.
The output file OUT2.txt will contain 5 lines – the total number of factors in the number.
3
4
5
12
32
0
2
0
3
5