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Lesson 15 of 17
  • Year 7

Highest common factor with algebraic terms

I can identify the highest common factor of two (or more) algebraic terms.

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Lesson 15 of 17
New
New
  • Year 7

Highest common factor with algebraic terms

I can identify the highest common factor of two (or more) algebraic terms.

Lesson details

Key learning points

  1. The highest common factor of two numbers can be found.
  2. Common factors of two terms can be found.
  3. It is possible to identify the highest common factor of two algebraic terms.
  4. It is possible to identify the highest common factor of more than two algebraic terms.

Keywords

  • Factor - A factor is a term which exactly divides another term.

  • Highest common factor - The highest common factor of two or more terms which can be divided by all other possible common factors.

  • HCF - HCF is an abbreviation for highest common factor.

  • Factorise - Factorise means to express a term as the product of its factors.

Common misconception

That factors only apply to whole numbers and a factor needs to be a whole number.

Whilst this is true for numerical factors, the factors of 7ab are 1, 7, a, b, 7a, 7b and ab.


To help you plan your year 7 maths lesson on: Highest common factor with algebraic terms, download all teaching resources for free and adapt to suit your pupils' needs...

Decomposition is the word to use in this lesson. Link this to prime factorisation, where pupils decomposed 12 to 2x2x3. Think of algebraic terms decomposing too. What is 10ef^2 made up of? 2 x 5 x e x f x f. This will make future factorising easier.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
$$1, 5, x, y, xy, 5x, 5y$$ and $$5xy$$ are all __________ of the algebraic term $$5xy$$

variables
multiples
Correct answer: factors
constants

Q2.
List all the factors of 36.

2, 3, 4, 6, 9, 12, 18
1, 2, 3, 4, 9, 12, 18, 36
Correct answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
1, 2, 3, 4, 6, 9, 12, 16, 18, 36
1, 2, 3, 6, 9, 16, 18, 36

Q3.
What is the Highest Common Factor of 16 and 20?

320
8
Correct answer: 4
2
1

Q4.
Simplify $$6ac \times 3ab$$

$$9abc$$
$$9a^2bc$$
$$18abc^2$$
Correct answer: $$18a^2bc$$
$$18abc$$

Q5.
Select all the expressions which are always equal to $$12xy^2z$$

Correct answer: $$2xy \times 6yz$$
Correct answer: $$3xy \times 4yz$$
$$2xy \times 6xz$$
$$3xyz \times 6y$$
Correct answer: $$xyz \times 12y$$

Q6.
Use this Venn Diagram to find the HCF of 84 and 462.

An image in a quiz
7
2
22
Correct answer: 42
924

Assessment exit quiz

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6 Questions

Q1.
HCF is an abbreviation of Highest Factor.

Correct Answer: Common, common

Q2.
List all the factors of $$8f$$.

$$8, f$$
$$1, 8, f, 8f$$
$$1, 2, 4, 8, f, 8f$$
Correct answer: $$1, 2, 4, 8, f, 2f, 4f, 8f$$
$$1, 2, 4, 6, 8, f, 2f, 4f, 6f, 8f$$

Q3.
List all the factors of $$9y^2$$

$$1, 9, y, y^2$$
$$1, 9y^2, 3y, 3y^2$$
$$3, 9, y^2, 3y^2$$
Correct answer: $$1, 3, 9, y, 3y, 9y, y^2, 3y^2, 9y^2$$
$$3, 6, 9, y, 3y, 6y, 9y, y^2, 3y^2, 9y^2$$

Q4.
List all of the common factors of $$6xy$$ and $$18xz$$.

$$1, 2, 3, 6, x, 2x, 3x, 6x, xy, 2xy, 3xy, 6xy$$
Correct answer: $$1, 2, 3, 6, x, 2x, 3x, 6x$$
$$1, 2, 3, 6$$
$$x, 2x, 3x, 6x$$
$$6x$$

Q5.
Match the pairs of terms to their Highest Common Factor.

Correct Answer:$$8e$$ and $$12def$$,$$4e$$

$$4e$$

Correct Answer:$$9ef$$ and $$15df$$,$$3f$$

$$3f$$

Correct Answer:$$9ef$$ and $$15def$$,$$3ef$$

$$3ef$$

Correct Answer:$$8de^2$$ and $$12d^2ef$$,$$4de$$

$$4de$$

Correct Answer:$$4de^2$$ and $$12d^3e^2f$$,$$4de^2$$

$$4de^2$$

Q6.
Use the Venn Diagram to find the HCF of $$20abc^2$$ and $$25a^2c^3$$

An image in a quiz
Correct answer: $$5ac^2$$
$$5a^2c$$
$$5ac$$
$$4b$$
$$100a^2bc^3$$