The number of distinct prime divisors of the number (256)^3-(130)^3-(126)^3

Question

a)10 b)5 c)8 d)15

Answer 1

12579840 = 1257984 * 10

= 4 * 314496 * 2 * 5

= 2 * 2 * 2 * 157248 * 2 * 5

= 2 * 2 * 2 * 2 * 2 * 39312 * 2 * 5

= 2 * 2 * 2 * 2 *2 * 2 * 2 * 9828 * 2 * 5

= 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 5 * 2457

= 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 5 * 3 * 819

= 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 5 * 3 * 3 * 273

= 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 5 * 3 * 3 * 3 * 91

2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 5 * 3 * 3 * 3 * 7 * 13

So the prime factors are 2, 3, 5, 7, and 13