Fundamental theorem of arithmetic

The fundamental theorem of arithmetic is the statement that every positive integer has a unique prime number factorization. For instance, we can write

6936 = 2³ * 3 * 17²

and there is no other such factorization of 6936 into prime numbers, except for reorderings of the above factors.

Knowing the prime number factorization of a number gives complete knowledge about all factors of that number. For instance, the above factorization of 6936 tells us that the positive factors of 6936 are of the form

2^a * 3^b * 17^c

with 0 ≤ a ≤ 3, 0 ≤ b ≤ 1, and 0 ≤ c ≤ 2. This yields a total of 4*2*3 = 24 positive factors.