# Factors and Multiples

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Prime Numbers are a special group of numbers that only have two factors. That is, prime numbers are numbers that can only be divided perfectly by two distinct numbers: 1 and themselves.

A factor is a whole number, an integer, that will divide another number exactly. Factors can be identified by discovering factor pairs of a number which are numbers that when multiplied together produce the number being inspected. For example, 1 and 24, 2 and 12, 3 and 8, and 4 and 6 are all factor pairs of 24 which means that the list of factor of 24 is 1, 2, 3, 4, 6, 8, 12 and 24.

The Highest Common Factor (HCF) is the largest common factor between two or more numbers. To find the HCF between two numbers, use a tree diagram to break down numbers into their prime factors and calculate the product of the common prime factors of both numbers. Prime factors are the smallest prime numbers that when multiplied produce the number being inspected. Alternatively, use a Venn Diagram to list the prime factors of the two numbers to find their HCF as the product of the common prime factors of both numbers. Both methods are shown below.

Multiples refer to the numbers in the times table of any number. For example, 15 is a multiple of 5 and it is also a multiple of 3. 15 can, then, be said to be a common multiple of 5 and 3.

The lowest Common Multiple (LCM) is the smallest common multiple between two numbers. To find the LCM between two numbers, use a tree diagram to break down numbers into their prime factors and calculate the product of the Highest Common Factor (HCF) and the prime factors left behind after calculating the HCF. Prime factors are the smallest prime numbers that when multiplied produce the number being inspected. Alternatively, use a Venn Diagram to list the prime factors of the two numbers to find the LCM as the product of the numbers in all sections of the Venn diagram.

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