--- title: "Factor Pairs & Commutativity" description: "Recognise and use factor pairs and commutativity in mental calculations" canonical: https://lightmysky.com/learn/mathematics/factor-pairs-and-commutativity-mt_nZkL5-XjRX source: https://lightmysky.com/learn/mathematics/factor-pairs-and-commutativity-mt_nZkL5-XjRX.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Factor Pairs & Commutativity Recognise and use factor pairs and commutativity in mental calculations Subject: Mathematics · Area: Multiplication & Division · Ages 8 to 9 Page: https://lightmysky.com/learn/mathematics/factor-pairs-and-commutativity-mt_nZkL5-XjRX ## Ready when they can - 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 ## Lesson: Factor Pairs and Switching the Order 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. *(drawing: This array has 4 rows of 6 dots, one factor pair for 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. **Example.** 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. **Tip.** 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. **Recap.** Factor pairs multiply to make a number, and commutativity lets you swap the order to make the math easier. ## Practice 17 questions on this page, each with its working shown. ## Needs first - [All times tables to 12×12](https://lightmysky.com/learn/mathematics/all-times-tables-to-12-12-mt_K5jM7vlVhA) - [Properties of Operations](https://lightmysky.com/learn/mathematics/properties-of-operations-mt_Lb2ZnMdkYR) ## Opens up - [Factors, multiples, and primes](https://lightmysky.com/learn/mathematics/factors-multiples-and-primes-mt_FHIAv6dfhU)