III Primes

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. $2 \times 3 \times 5$.