Prime factors

by Dominic Ford

Every positive integer can be written as the product of a sequence of prime numbers.

It can be proven that these sequences are unique: every integer can be written in one, and only one, way. This is called the fundamental theorem of arithmetic.

For example, each prime number can only be written by multiplying itself by one, e.g. $$1 \times 7$$.

The number 8 can be made by multiplying $$2 \times 2 \times 2$$, but not by multiplying any other prime numbers.