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• Factors are integers that divide exactly into a number.

• Factors can be found by listing them out, using arrays or using factor trees.

• A factor pair is a set of two factors. When multiplied together, the pair give a particular product. A square number has one factor pair consisting of one factor multiplied by itself.

• A number that has more than two factors is a composite number. This can be expressed as a unique product of prime factors. This is useful when finding the highest common factor (HCF) and lowest common multiple (LCM) of large numbers.

• To be able to find factors and write a number as a product of prime factors, having knowledge of powers and indices is useful.

1. Draw different rectangular arrays with the right amount of squares. Eg, to find the factors of 15, draw arrays with 15 squares

   • The first rectangle will always be 1 x the number you are finding factors for.

   • For the next rectangles, consider whether they can have a dimension of 2, 3, 4 etc. Use your understanding of divisibility rules to help.

2. Each time you draw a rectangle, two factors are found. These are a factor pair.

3. Sometimes one of the rectangles is a square with equal side lengths. This happens when the number is a square number. The same factor is found twice - therefore only one factor is actually found. Eg, 5 × 5 = 25 and 5 is a factor of 25

Remember: To find all the factor pairs, it is not necessary to draw every rectangle. Eg, a 5 x 2 rectangle and a 2 x 5 rectangle are the same rectangle in a different orientation. Only one of these rectangles is needed to get the factor pair of 2 and 5. Either rectangle can be picked.

A factor tree is made up of factor pairs that are numbers greater than 1. A prime number does not produce a factor tree because one of its factors is 1 and the other is itself so the number would be repeated – the factor tree would not grow.

1. Write the number at the top of the factor tree.

2. Draw two branches from the number to split the number into a pair of factors, greater than 1

3. Write each factor at the end of each branch.

   • If a factor is a prime number, the branch does not extend any further and the factor is circled to show this.

   • If the factor is not a prime number, it is split into a further pair of factors, greater than 1

4. This process continues until the branches all end in prime numbers. These are prime factors of the number.

Remember: the factor tree of a number can look different, but the numbers at the end of the branches will be the same.

To write a number as a product of prime factors, the number is written as the result of multiplying its prime factors together.

1. Draw a factor tree.

2. Write the number equal to the factors multiplied together in numerical order.

3. When a number occurs more than once, this can also be written in index form (with powers).

Writing a number as a product of its prime factors can be helpful when finding the highest common factor (HCF) and lowest common multiple (LCM) of large numbers.

Practise what you've learned about finding the factors of a number with this quiz. You may need a pen and paper for some of these questions.

Finding factors and factor pairs can be useful in many different situations in real life.

For example, a couple are getting married and are planning their wedding. They have 72 guests coming who all need a seat. The tables can seat up to 12 people.

By using factor pairs, the couple can choose different combinations to suit their friends and family:

• 12 tables of 6 guests

• 9 tables of 8 guests

• 8 tables of 9 guests

• 6 tables of 12 guests