Prime, Square and Cube Numbers

Prime numbers

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A prime number is a number with exactly two factors. A prime number is 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 (\(1 \times 11 = 11\)). 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 (\(1 \times 15 = 15, 3 \times 5 = 15\)). 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 under 30 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

Example

Identify the prime number 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.

\(45 = 5 \times 9\) 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 answer when an 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 \(1 \times 1 = 1\).

The second square number is 4 because \(2 \times 2 = 4\)

The third square number is 9 because \(3 \times 3 = 9\), 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

What is the twentieth square number?

20 squared = \(20 \times 20 = 400\).

So 400 is the twentieth square number.

Cube numbers

A cube number is the answer 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.

Cubes representing cubed numbers. 1 x 1 x 1 = 1. 2 x 2 x 2 = 8. 3 x 3 x 3 = 27.

The first cube number is 1 because \(1 \times 1 \times 1 = 1\).

The second cube number is 8 because \(2 \times 2 \times 2 = 8\).

The third cube number is 27 because \(3 \times 3 \times 3 = 27\), and so on.

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

Example

What is the tenth cube number?

10 cubed = \(10 \times 10 \times 10 = 1000\).

So 1000 is the tenth cube number.

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Multiples, factors, powers and roots - OCRPrime, Square and Cube Numbers