- A 'natural number' is a non-negative whole number. For example, '0', '1', and '23' are natural numbers, but '-7'Â and '3.14' are not.
- A 'factor' of an natural number 'n' is a natural number that divides 'n' with no remainder. For example, '1', '2', '3', '4' and '6' are factors of '12', but '5' is not.
- A 'prime number' is a natural number 'n' that has exactly two factors: '1' and 'n'. For example, '5' is a prime number (its factors are '1' and '5') but '6' is not (its factors are '1', '2', '3' and '6'). Note that '1' is not considered to be a prime number, as it has only one factor.
- A 'prime factor' of a natural number 'n' is a factor of 'n' that is itself a prime number. For example, '2' and '3' are prime factors of '12', but '1', '4' and '6' are not.
- The 'prime factorisation' of a natural number 'n' is the multiset of prime factors of 'n' whose product equals 'n'. For example, the prime factorisation of '12' is '{2, 2, 3}' (because '2' and '3' are prime numbers, and '2 × 2 × 3 = 12'). Each natural number has a unique prime factorisation.