Factors, multiples, squares and cubes (age 9+)
Solve problems involving multiplication and division using knowledge of factors, multiples, squares, and cubes
What a learner can do afterwards
- 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
1 · Read
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.
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.
Find two square numbers that add to make 100. Try 36 (which is 6 × 6) and 64 (which is 8 × 8). 36 + 64 = 100.
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.
Factors, multiples, and squares are shortcuts: use them to break hard problems into easy steps.
More to read
2.4 Find Multiples and Factors
A multiple of a number is what you get when you multiply it by a whole number. The multiples of 6 are 6, 12, 18, 24 and so on. A factor works the other way round: factors of 12 are the whole numbers that divide into 12 exactly, which are 1, 2, 3, 4, 6 and 12. To test if 156 is a multiple of 6, divide 156 by 6. Since 6 x 26 = 156 with nothing left over, 156 is a multiple of 6.
2.5 Prime Factorization and the Least Common Multiple
A prime number has exactly two factors: 1 and itself. So 13 is prime, but 15 is not because 3 x 5 = 15. The number 1 is special and is not prime, since it has only one factor. Breaking numbers into factor pairs helps with bigger multiplications too. For 24 x 25, split 24 into 6 x 4, then work out 6 x (4 x 25) = 6 x 100 = 600.
Factors, multiples, and patterns: FAQ
Square numbers come from multiplying a whole number by itself. Since 8 x 8 = 64 and 6 x 6 = 36, the pair 64 and 36 adds to 100. Spotting squares like 49 = 7 x 7 makes mental maths quicker. Factor pairs, multiples, primes and squares all fit together. Each one is a different way of asking how numbers multiply and divide.
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17 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.