Factors and multiples — Mathematics, 7–10 years
See how numbers fit together through equal groups and repeated jumps. Mathematics, 7–10 years.
What factors and multiples show
Factors are numbers that fit exactly into another number, making equal groups with nothing left over. Multiples are the numbers you meet when you keep adding the same number: 5, 10, 15 and 20 are multiples of 5. They show how numbers can be built and shared.
Why we look for them
When people needed to arrange objects in neat rows or make fair teams, they had to know which group sizes would work. Factors answer “Can this number be split evenly?” and multiples answer “When will two counting patterns meet?” These ideas grew from practical counting, sharing and measuring.
Finding the factors of 24
Start with 1: 1 × 24 makes 24, so 1 and 24 are factors. Try 2: 2 × 12 works; try 3: 3 × 8 works; try 4: 4 × 6 works. The factor pairs are 1 and 24, 2 and 12, 3 and 8, and 4 and 6, so all the factors are 1, 2, 3, 4, 6, 8, 12 and 24.
A factor is not always smaller
It is easy to list only the small numbers and forget the matching partners. For 24, someone may write 1, 2, 3 and 4 because those are the numbers tested first. But 24 itself is a factor too: 24 × 1 = 24. Looking for pairs prevents this reasonable shortcut from hiding answers.
Where they help
A baker can use factors to put 24 cupcakes into equal boxes: 2 boxes of 12, 3 of 8, 4 of 6, or 24 of 1. Multiples help with repeated events, too. If one light flashes every 4 seconds and another every 6 seconds, they flash together again after 12 seconds.
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