---
title: "Factors, multiples, squares and cubes (age 9+)"
description: "Solve problems involving multiplication and division using knowledge of factors, multiples, squares, and cubes"
canonical: https://lightmysky.com/learn/mathematics/factors-multiples-squares-and-cubes-age-9-mt_0Wg5F97osg
source: https://lightmysky.com/learn/mathematics/factors-multiples-squares-and-cubes-age-9-mt_0Wg5F97osg.md
retrieved: 2026-09-12
---

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# Factors, multiples, squares and cubes (age 9+)

Solve problems involving multiplication and division using knowledge of factors, multiples, squares, and cubes

Subject: Mathematics · Area: Multiplication & Division · Ages 9 to 10
Page: https://lightmysky.com/learn/mathematics/factors-multiples-squares-and-cubes-age-9-mt_0Wg5F97osg

## Ready when they can

- Is 156 a multiple of 6? Explain how you know
- Find two square numbers that add to make 100
- Use factor pairs to simplify 24 × 25 as 6 × (4 × 25) = 6 × 100 = 600

## Lesson: Using factors, multiples, and squares to solve problems

You already know your factors, multiples, squares, and cubes. Now you get to use them as tools. They help you check big numbers fast and turn hard multiplication into easy steps.

**Example.** Is 156 a multiple of 6? A multiple of 6 must be a multiple of 2 and a multiple of 3. 156 is even, so it passes the first test. Add its digits: 1 + 5 + 6 = 12, and 12 is a multiple of 3. 156 passes both tests, so it is a multiple of 6.

*(drawing: 24 splits into a factor pair, 6 and 4. Swapping a hard number for its factor pair can make multiplication easier.)*

**Example.** Find two square numbers that add to make 100. Try 36 (which is 6 × 6) and 64 (which is 8 × 8). 36 + 64 = 100.

**Tip.** When a problem looks hard, look inside it for a shortcut: a factor pair, a multiple you know, or a square you remember. Break the number apart, solve the easy pieces, then put them back together.

**Recap.** Factors, multiples, and squares are shortcuts: use them to break hard problems into easy steps.

## Practice

17 questions on this page, each with its working shown.

## Needs first

- [Factors, multiples, and primes](https://lightmysky.com/learn/mathematics/factors-multiples-and-primes-mt_FHIAv6dfhU)
- [Square and cube numbers](https://lightmysky.com/learn/mathematics/square-and-cube-numbers-mt_gxCIASSezX)

## Opens up

- [Factors, multiples, and primes (age 11+)](https://lightmysky.com/learn/mathematics/factors-multiples-and-primes-age-11-mt_xhoOWnhtHq)