Difference between factors and prime factors

I'll add that in general, if a problem just wants you to figure out how many prime factors (or 'unique prime factors', or just plain factors) there are, they have to be specific about which one they mean. Remember that 1 is a factor of every number, but because 1 isn't prime, it's never a prime factor!

But if you're solving a Number Properties problem that doesn't ask you specifically for the number of factors, but instead asks you a more general question about divisibility, you probably want the prime factorization specifically. In fact, I'd go so far as to say that every time you see a NP problem with a large integer in it, you should break it down to its prime factors right away. It's pretty rare to have to calculate the whole list of factors in the course of solving a more general problem, but pretty common to have to do a prime factorization.

Factors could be any numbers whose product is equal to the product (the result of multiplication)
for example, factors of 12 are: 1*12 = 2*6 = 3*4

On the other hand, the prime factors are also factors of a given number but they must prime (2, 3, 5, 7, 11, 13, 17, ...)
For example, the prime factors of 12 = (3*4) = 3*2*2 = 2^2+3 [notice here all the factors are prime numbers 2 and 2]


Good luck