936 as a product of prime numbers?

Answer 1

Every number can be 'uniquely' factored into prime factors - this is called the Fundamental Theorem of Arithmetic.

The simplest way is to just run through the primes 2, 3, 5, 7, 11, 13, 17, 19, 23 ... until the number is factored. You can stop if the remaining (unfactored) number is less than the square of the largest prime you have tried (529 with the above list, but it does get harder to find them - look up Sieve of Eratosthenes for a way to generate them).

So 936 = 2 x 468
-- 468 = 2 x 234
-- 234 = 2 x 117
-- 117 = 3 x 39
-- 39 = 3 x 13
and 13 is prime.

963 = 2 x 2 x 2 x 3 x 3 x 13 or 2^3 x 3^2 x 13.

Or you could say its factors are 2 (three times), 3 (twice) and 13.