Factor Pairs & Commutativity
Recognise and use factor pairs and commutativity in mental calculations
What a learner can do afterwards
- List all factor pairs of a given number (e.g. 24: 1×24, 2×12, 3×8, 4×6)
- Use commutativity to reorder a multiplication for easier mental calculation
- Explain what a factor pair is and how commutativity helps
The lesson
A factor pair is two numbers that multiply together to make another number. For 24, one factor pair is 4 and 6, because 4 times 6 equals 24.
Numbers can have several factor pairs. 24 also comes from 1 and 24, 2 and 12, and 3 and 8. Multiplication also follows a rule called commutativity: you can swap the order of two numbers and the answer stays the same, so 6 times 4 equals 4 times 6.
To multiply 4 times 15 in his head, Ben splits 15 into its factor pair 5 and 3. Then he multiplies 4 times 5 to get 20, and 20 times 3 to get 60.
When a number feels hard to multiply, look for an easy factor pair to split it into. Pick the split that gives you numbers you already know well.
Factor pairs multiply to make a number, and commutativity lets you swap the order to make the math easier.
Watch it
Where it sits
This opens up
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.