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HCF of Algebraic Expressions

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HCF of Algebraic Expressions

Find the highest common factor (HCF) of each pair. For algebraic terms, find the HCF of the numbers and include only variables that appear in every term, using the smallest power. Show a factorisation or other clear working.

Spot the shared factor

A workshop is sorting materials into equal-sized groups. Find the HCF for each pair, then use your results to help with the challenge question.

1.Find the HCF of 18 and 30. Write one factorisation of each number to show how you know.

2.Find the HCF of 24a and 36a². Include the common variable factor in your answer.

3.A rectangular sign has side lengths 42x² cm and 56x cm. What is the HCF of these algebraic terms?

4.Which expression is the HCF of 45m³ and 60m²? Choose one.

15m²
15m³
5m²
15

Factor and explain

Look closely at coefficients and variable powers. A variable that is missing from even one term cannot be part of the HCF.

5.Find the HCF of 32p²q and 48pq³. Show how you choose the power of each variable.

6.Find the HCF of 28r² and 42s². Explain why no variable belongs in the HCF.

7.True or false? The HCF of 36x²y and 54xy³ is 18xy. Correct the statement if it is false.

TrueFalse

8.Complete the factorisation: 20a² + 30a = ( + ). Find the HCF first.

Put the HCF to work

Use the common factor to simplify expressions and solve a practical grouping problem.

9.Factorise 63x³ − 81x² by taking out the HCF. Check by expanding your answer.

10.A craft group has 48 blue beads and 72 green beads. They want to make the greatest possible number of identical kits, using every bead. How many kits can they make, and how many of each colour go in each kit?

11.A student says the HCF of 24x²y and 40xy² is 8x²y². Identify the mistake and give the correct HCF.