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11 and 33 are factors of 66.

Level 3-4 Algebra - Factors

Learn to factorise expressions by spotting common factors and pairs that multiply to a number. These skills simplify algebra and unlock quicker solutions in KS3 Maths.

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Fascinating Fact:

The expression x² + 5x + 6 can be factorised into (x + 2)(x + 3), because 2 and 3 multiply to 6 and add to 5.

In KS3 Maths, factorising reverses expanding brackets. You’ll find common factors, split middle terms, and use number pairs to rewrite expressions as products, making algebra shorter and easier to work with.

Key Terms

Factor: A number or expression that multiplies with another to make a product, e.g. 3 is a factor of 12.
Common factor: A factor shared by every term in an expression, used to take something outside brackets.
Factorising: Rewriting an expression as a multiplication of simpler parts, such as x² + 5x + 6 = (x + 2)(x + 3).

Frequently Asked Questions (Click to see answers)

How do I factorise a quadratic like x² + bx + c?

Find two numbers that multiply to c and add to b. Use them to split the middle term or write the factor pairs directly, e.g. x² + 5x + 6 = (x + 2)(x + 3).

What is the first step when factorising any expression?

Always check for a greatest common factor (GCF) first. Taking out the GCF simplifies the expression and makes further factorising easier.

How is factorising different from expanding brackets?

Expanding multiplies brackets out to a single expression. Factorising is the reverse process: rewriting an expression as a product of brackets or factors.

Try These Related Quizzes

1 .

Which of these sets of numbers are not all factors of 100?

2, 4, 10

5, 10, 20

2, 20, 50

20, 40, 50

In the correct answer, 40 cannot be divided into 100 and give a whole number as the result

2 .

Which of these is not a factor of 60?

The 25 times table goes from 50 to 75. 60 is not in it

3 .

Which of these is a factor of 66?

22 x 3 = 66

4 .

Is 4 a factor of 21?

Yes

Seldom

Often

If you divide 4 into 21 the answer is 5.25. Because the answer is NOT a whole number, 4 is NOT a factor of 21

5 .

Which of the following is a factor pair of 32?

2 and 14

2 and 16

2 and 18

2 and 20

An easy one this. 2 x 16 = 32

6 .

Which of these is not a factor of 80?

26 x 3 = 78 and 27 x 3 = 81. 80 cannot be divided by 3 to a whole number

7 .

Which of these sets of numbers are all factors of 80?

2, 4, 8, 16

2, 4, 8, 12

4, 8, 16, 18

2, 4, 14, 20

In all the incorrect answers there is a number that will not divide into 80 and give a whole number as the result

8 .

Which of these is a factor of 33?

11 is the only one that can be divided into 33 and produce a whole number

9 .

Which of these is a factor of 70?

7 x 10 = 70

10 .

A number which divides exactly into two other numbers is what sort of factor of those numbers?

Cheap

Expensive

Common

Frequent

The two numbers have that factor in common

You can find more about this topic by visiting BBC Bitesize - Prime numbers, factors and multiples

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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