## Primes

Prime numbers are numbers that are divisible into a whole number only by 1 and itself. e.g. 6 is not a prime number because it can be divided cleanly by 1, 6, 3 and 2. 5 on the other hand is a prime number because it can only neatly divided by 1 and 5. 2 is the only even number prime number because every other even number is divisible by 2.

*Composite numbers* are all numbers that are not prime. They can be interpreted as products of various factors.

## Prime factorization

Composite numbers can be decomposed into factors of smaller integers, e.g $30 = 2 \times 15$. Further decomposing composite factors yields a tree with a prime number in each leaf node: $15 = 3 \times 5$. That process is called *prime factorization*. Every composite number can be written as a product of its prime factors, e.g. $2 \times 3 \times 5$.