What is a factor?

• A factor is an integerthat divides exactly into a whole number without a remainder. Eg, 3 is a factor of 12

• A factor pair is a set of two factors. When multiplied together, they give a particular product. Eg, 3 and 4 have a product of 12, so 3 and 4 are a factor pair of 12

• A multiple is a number that is in a particular times table. Eg, 12 is a multiple of 3 because 12 is in the 3 times table. 12 is also a multiple of 4 because 12 is also in the 4 times table.

• Knowing multiplication and division facts supports understanding of factors and factor pairs. Knowing divisibility rules is helpful in identifying multiples of a particular number.

• A factor is an integer that divides exactly into a selected whole number with no remainder.
• Every whole number greater than 1 has two or more factors.
• When a number is divided by one factor, the answer is another factor. The two factors are called a factor pair.
• The product of each factor pair is equal to the number.

Remember: The first factor pair is always 1 and the number itself.

When finding all the factor pairs of a number, there is a methodical approach you can take:

• Remember that the first factor pair is always 1 and the number itself.
• Consider whether the number is divisible, in turn, by 2, 3, 4 etc. Use your understanding of the rules of divisibility and times tables up to 12 x 12 to help.
• When a number is divided by one factor, the answer is another factor. The two factors are called a factor pair.
• The product of each factor pair is equal to the number.

Remember: all the factors are found when the next value is part of an established factor pair.

• A multiple is a whole number in the times table of a selected whole number.
  Eg, any number in the 4 times table is a multiple of 4. Multiples of 4 include 4, 8, 12, 16, 20 …
• There are an infinite number of multiples for any whole number.

Try this quiz to practise finding factors, factor pairs and multiples.

Factors

Factors are used every day when we divide or share something into equal pieces. Eg, an outdoor adventure company who organises group activities may need to split a large group of people into smaller groups for each activity.

A group of 24 people could be split into:

• 6 groups of 4 (6 x 4 = 24)
• 8 groups of 3 (8 x 3 = 24)
• 12 pairs (12 x 2 = 24)

Different activities may need different sized groups. As 24 has several factor pairs, organising the activities is easier than if there were 25 people.

Multiples

A baker will bake in batches to minimise food waste. Eg, if cupcakes are packed in boxes of 6, the batches baked will be a multiple of 6. A small batch may be for 24 cupcakes, a large batch bake could be for 120 cupcakes.