Myths about teaching can hold you back
- Year 7
Highest common factor
I can use the prime factorisation of two or more positive integers to efficiently identify the highest common factor.
- Year 7
Highest common factor
I can use the prime factorisation of two or more positive integers to efficiently identify the highest common factor.
Lesson details
Key learning points
- Common factors can be found by comparing the products of their primes.
- The highest common factor of two numbers can be found by comparing the prime factorisation of both numbers.
- Sometimes a Venn diagram can help identify the highest common factor of two numbers.
- The highest common factor of more than two numbers can be found using prime factorisation.
Keywords
Prime factorisation - a method to find the prime factors of a given integer
Highest common factor - The highest common factor of two or more integers which can be divided by all other possible common factors
HCF - an abbreviation for highest common factor
Common misconception
Common factors are put into the intersection of the Venn diagram twice instead of once.
Encourage students to check that the product of the factors in each set is the correct integer.
To help you plan your year 7 maths lesson on: Highest common factor, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 7 maths lesson on: Highest common factor, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 3 maths lessons from the Properties of number: factors, multiples, squares and cubes unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.A number is the product of two repeated integers.
Q2.Write $$2^3\times3\times5^2$$ as an integer.
Q3.True or false? $$2^5\times3^3\times5$$ is an even integer
Q4.True or false? $$2\times3\times5^2$$ is a multiple of 10
Q5.Which of the following is a multiple of 6?
Q6.Which of the following is a square number?
Assessment exit quiz
6 Questions
Q1.The C in HCF stands for
Q2.$$7^5$$ is a factor of an integer. Which of the following are also factors of the same integer?
Q3.Which of the following is a factor of $$2^4\times3^2\times5^2$$ and of $$2^3\times3^4\times5$$?
Q4.The HCF of 120 and 630 is
Q5.The HCF of 42, 60 and 90 is
Q6.The HCF of 36, 54 and 270 is 18. The missing prime factor in the Venn diagram is
