Prime and Composite

Some numbers have only two factors: 1 and themselves.

Prime number has exactly two factors: 1 and itself.

Most numbers have more.

Composite number has more than two factors.

A prime makes one rectangle

7 squares can only make a 1 by 7 rectangle. 12 squares make three different ones.

One is neither

1 has only one factor, itself. Prime means exactly two, so 1 is not prime.

What makes a number prime

A prime number has exactly two factors: 1 and itself. So 7 is prime, because only 1×7 makes it. A composite number has more than two factors, like 12 with its 1, 2, 3, 4, 6 and 12. Prime numbers build exactly one rectangle: a single row.

Why 1 is neither

1 has only one factor — itself. That fails the definition of prime, which requires exactly two. It is not composite either, since it has fewer than three factors. So 1 sits outside both categories, by definition rather than by accident.

Testing a number

To check whether 51 is prime, try dividing by 2, 3, 5, 7 in turn. 51 ÷ 3 = 17, so it is composite. You only need to test up to the point where the factors would start repeating, which keeps the work short.

Primes are the building blocks

Every whole number bigger than 1 can be written as a product of primes, and in only one way: 12 = 2 × 2 × 3. Primes are to numbers roughly what atoms are to substances, which is why mathematicians care about them far beyond Grade 4.