At GCSE level you will come across vocabulary such as **real** numbers, **integers**, **natural** numbers, **indices**, **factors**, **multiples**, **prime**, **square** and **cube** numbers. Knowing what all of this means is essential.

**Real**numbers are the set of**all numbers**, including integers, fractions, rational and irrational numbers- All numbers dealt with at GCSE level are considered real numbers
- You may see the symbol ℝ used to denote real numbers

**Integers**are all**whole numbers**, they can be positive, negative or zero- For example, …, -3, -2, -1, 0, 1, 2, 3, … are all integers
- You may see the symbol ℤ used to denote integers

**Natural**numbers are the set of all**positive integers**- They are sometimes thought of as the counting numbers
- For example, 1, 2, 3, … are the natural numbers
- You may see the symbol ℕ used to denote natural numbers

- A
**factor**is a number that divides into another number exactly- For example, the factors of 18 are 1, 2, 3, 6, 9, and 18
- Every number has at least two factors, itself and 1

- A
**multiple**is a number that is in the times table of another number- Every non-zero number has an infinite number of multiples, they go on forever
- For example, the multiples of 3 are 3, 6, 9, 12, 15, 18 and so on

- A
**prime**number is a number which has exactly two factors, itself and 1- 1 is not a prime number, as it only has one factor
- 2 is the only even prime number
- You should remember at least the first ten prime numbers
- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

- A
**square**number is the number derived from multiplying a number by itself- For example, 3 × 3 = 9, so 9 is a square number
*a*×*a*can be denoted*a*^{2}- You should remember at least the first twelve square numbers
- 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144

- A
**cube**number is the number derived from multiplying a number by itself twice- For example, 3 × 3 × 3 = 27, so 27 is a cube number
*a*×*a*×*a*can be denoted*a*^{3}- You should remember at least the first five cube numbers
- 1, 8, 27, 64, 125

- An
**index**(**indices**plural) is a way of writing a string of multiplications of the same number neatly- They are often called powers, and sometimes exponents
- For example, 3 × 3 × 3 × 3 is the number 3 multiplied by itself 4 times and can be written 3
^{4} *a*×*a*×*a*×*a*×*b*×*b*×*b*×*b*×*b*can be written in index form as*a*^{4 }×*b*^{5}

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