the number of prime factors of (3 x 5)12 (2 x 7)10 (10)25 is:

Express the given number N as a product of prime numbers:

N
=

A prime factor of N is obtained by multiplying (none or one or two or three or four or five of 2s ) * (none or one or two of 3s ) * (none or one or more of 5s ) * (none or one 7 )

So the number of distinct prime factors will be

= (1+5)(1+2)(1+5)(1+1) = 6 * 3 * 6 * 2

= 216