Curriculum Hub → Maths Lessons → Number → Factor Pairs
Knowing how to find the factors of a number helps students connect with topics such as prime numbers, square numbers and perfect numbers. You can also link factors to area, perimeter and algebra and the highest common factor of a pair of numbers has clear applications in fractions and real-life problems.
In this blog I show five practical ways I connect factor pairs to other areas of maths, both in class and as homework activities.
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At the start of a lesson on primes, I challenge students to think of at least ten numbers that have exactly two factors. I avoid phrasing this as “a factor of 1 and itself”, because that description also includes the number 1, which is not prime.
A common misconception when listing primes is to include 9, 21 and 27. By finding primes through factor pairs, students are much less likely to fall into that trap.
A useful homework activity is to ask students to list the first twelve numbers that have an odd number of factors. This consolidates their learning of factor pairs and prepares them for the next lesson on square numbers.
As an extension, ask students to explain why these numbers have an odd number of factors. The discussion naturally leads to the idea that one factor is repeated when the number is a square.
A perfect number is a positive integer equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself.
Finding perfect numbers is my favourite plenary when teaching factor pairs. Students use trial and improvement to search for them, which embeds the skill of listing factors. The activity is easy to differentiate:
To consolidate factor pairs at the start of the following lesson, I present a rectangle with a fixed area. Students can earn a House Point for finding the dimensions of a rectangle with:
More able students often consider decimal dimensions, such as 0.1 cm by 240 cm, giving a perimeter of 480.2 cm. Very few students find the smallest perimeter using √24 cm² which makes for a powerful teaching point when you reveal it.
A strong plenary when teaching algebraic products is to find factor pairs of an algebraic expression for example, the factor pairs of 30x²y.
Students typically list 30 and x²y, or 30x² and y, but often forget pairs such as 5x² and 6y. As a further extension, give a rectangle with area 30x²y and ask students to investigate different possible perimeters.
The Factor Pairs of Numbers and Terms lesson pack includes a ready-to-teach PowerPoint, differentiated worksheet and student handout. Mr Mathematics Membership unlocks this pack plus full schemes of work and hundreds of lessons across KS3 to A-Level.
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