Prime numbers, factors and multiples are essential building blocks for a lot of number work. Knowledge of how to use these numbers will improve arithmetic and make calculations more efficient.

A prime number is a number with exactly two factors. Prime numbers are only divisible by 1 and itself. Another way to think of prime numbers is that they are only ever found as answers in their own times tables.

11 is a prime number because the only factors of 11 are 1 and 11 (). No other whole numbers can multiply together to make 11.

15 is not a prime number because the factors of 15 are 1, 3, 5 and 15 (). 15 has more than 2 factors, so it is not a prime.

1 is not a prime number as it only has one factor - itself.

2 is the only even prime number. Every other even number has 2 as a factor, and so will not be prime.

There are an infinite number of prime numbers. The prime numbers less than 30 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

Example

Identify the prime number(s) from this list: 42, 43, 44, 45

42 and 44 are even, and so cannot be prime as they both have 2 as a factor.

and so is not prime.

43 is prime as the only factors of 43 are 1 and 43.

Square Numbers

A square number is the number given when an integer is multiplied by itself. It is called a square number because it gives the area of a square whose side length is an integer.

The first square number is 1 because .

The second square number is 4 because

The third square number is 9 because , and so on.

The first fifteen square numbers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196 and 225.

Example

Work out the value of 20 squared?

20 squared = .

So 400 is a square number.

Cube numbers

A cube number is the number given when an integer is multiplied by itself, then multiplied by itself again. It is called a cube number because it gives the volume of a cube whose side length is an integer.

The first cube number is 1 because .

The second cube number is 8 because .

The third cube number is 27 because , and so on.

The first five cube numbers are: 1, 8, 27, 64 and 125.