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Common factors

Factorising an expression simplifies it in some way. Factorising is the reverse of expanding brackets.

Common factors

If you cannot remember what factors are, or how to find them, have another look at Re-arranging symbols.

When multiplying out 3(4x - 7), the rule was to multiply everything in the brackets by 3.

This gives 3(4x - 7) = 12x - 21

So, when asked to factorise 12x - 21 look for the Highest Common Factor (HCF) of 12 and 21 (in this case 3) and divide both terms by this number.

12x - 21 = 3(4x - 7)


Factorise 24a + 16

toggle answer


24a + 16 = 8(3a + 2)

Therefore, the HCF of 24 and 16 is 8.

Factorising Quadratics

You can also factorise quadratic expressions. For example x2+x can be factorised as x is a common factor to both terms.

x2+x = x (x+1)


Factorise 3p2 - 6p


  • 3p2 means 3 x p x p, and 6p means 6 x p.
  • The HCF of 3 and 6 is 3, and the HCF of p2 and p is p, so we divide both terms by 3p:

3p2 - 6p = 3p(p - 2)

Most people find expanding brackets easier than factorising, so always check that your answer is correct by multiplying out and seeing whether you have what you started with.

Back to Algebra index

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