Before you start using all of these different types of numbers you should make sure you know your tables. Even when calculators are available, it would be useful and make your work quicker if you could add, subtract and multiply the numbers from 1 to 10 in your head.

This section introduces a selection of types of numbers and mathematical operations.

The Words

The SUM of numbers is when they are added together.

The DIFFERENCE between numbers is when they are subtracted.

The PRODUCT of numbers is when they are multiplied.

For the calculation 10 ÷ 2 = 5

10 is called the DIVIDEND
2 is called the DIVISOR
5 is called the QUOTIENT

Multiples

The multiples of a natural number are formed by multiplying the number by 1, 2, 3, ...

e.g. Multiples of 5 are 5, 10, 15, 20, ...
Multiples of 11 are 11, 22, 33, 44, ...

The lowest common multiple of numbers is the lowest multiple that is shared by the numbers.

e.g. The lowest common multiple (LCM) of 4 and 6 is 12.
The lowest common multiple (LCM) of 3 and 5 is 15.

Factors

The factors of a natural number are the numbers that divide into it without any remainder.

e.g. Factors of 8 = {1, 2, 4, 8}
Factors of 30 = {1, 2, 3, 5, 6, 10, 15, 30}

The highest common factor (HCF) of numbers is the highest factor shared by the numbers.

e.g. Highest common factor of 8 and 12 is 4.
Highest common factor of 12 and 18 is 6.

Divisibility of Numbers

There are some useful "tricks" to help you decide whether a number is a factor of another number. This is called divisibility.

Click the numbers below to find out what they are.

Prime Factors

Natural numbers can be written as the product of prime numbers.

e.g. 30 = 2 x 3 x 5
12 = 2 x 2 x 3 = 2² x 3

Composite Numbers

Composite numbers are numbers with more than two factors. i.e. The non-prime numbers.

e.g. 12 is a composite number as it has six factors {1, 2, 3, 4, 6, 12}

Square Roots

The square root of a number, shown by the sign , is the positive number that, when multiplied by itself, gives the number.

e.g. and 

Squares

The square of a number is the number multiplied by itself.

e.g. 5 ² = 5 x 5 = 25

(-3) ² = -3 x -3 = 9

Reciprocals

The reciprocal of a number is equal to 

The reciprocal of 0 is not defined. i.e. The fraction ¹⁄₀ cannot be calculated.

To find the reciprocal of a fraction, turn the fraction upside down.

e.g.The reciprocal of ²⁄₅ is ⁵⁄₂

A number multiplied by its reciprocal always equals 1.

e.g. ³⁄₄ × ⁴⁄₃

Most calculators have a reciprocal button or 1/x

Standard Form

Numbers written in standard form are shown as the product of a number between 1 and 10 and a power of 10.

e.g. 327 = 3.27 × 10 ²

0.46 = 4.6 × 10 ^{- 1}

Standard form, sometimes called scientific notation, is often used in science to show very large or very small numbers.

Prime Numbers

A prime number has only two unique factors − itself and 1.

The only even prime number is 2.

1 is not a prime number.

The first eight prime numbers are {2, 3, 5, 7, 11, 13, 17, 19}