Use factors and remainders

See what is left after division, then find the numbers that divide exactly.

Count what is left over

Divide 14 into groups of 4. You can make 3 whole groups, with 2 left over: 14 = 4 × 3 + 2. Those 2 are the remainder. There are too few left to make another group of 4.

A positive factor divides a number with no remainder. Because 2 are left over, 4 is not a factor of 14. Every positive whole number has 1 and itself as factors.

4+4+4+2
3 whole groups of 4, with 2 left over.

Find factor pairs

Find pairs of positive whole numbers that multiply to 12: 1 × 12, 2 × 6 and 3 × 4. Each pair arranges all 12 squares into complete rows, with none left over.

The factors are 1, 2, 3, 4, 6 and 12: six in total. Include 1 and 12. Count each distinct number once, even if you write a pair in the opposite order.

1 × 122 × 63 × 4
Three pairs, six distinct factors of 12.

Count the factors of a new number

How many positive factors does 10 have? Find pairs that multiply to 10.

Remember to include 1 and 10. Count every distinct factor once.

Ten squares. Find all the positive factors.

Try it

How many positive whole-number factors does 10 have?

  1. 4
  2. 2
Show the answer

4

Correct. The factor pairs are 1 × 10 and 2 × 5. The distinct factors are 1, 2, 5 and 10, so there are 4.

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