Factors and Multiples

Study Sheet

Factors and Multiples

What divides evenly

Factors in Pairs

Concept
The Big Idea
3 rows of 4

Factors come in pairs that multiply to the number, which is why you only have to test up to the square root — after that the pairs repeat.

Example
The factors of 12

1×121 \times 12, 2×62 \times 6, 3×43 \times 4. So the factors are 1,2,3,4,6,121, 2, 3, 4, 6, 12 — six of them. Each pair is one possible array.

In Plain Terms & More Examples

Concept
In plain terms

A factor divides evenly with nothing left over; a multiple is what you get by counting up in steps of the number.

Example
The factors of 18

1×181 \times 18, 2×92 \times 9, 3×63 \times 6. So the factors are 1,2,3,6,9,181, 2, 3, 6, 9, 18.

Example
The first multiples of 4

Count up in fours: 4,8,12,16,20,…4, 8, 12, 16, 20, \dots