Indices and Factors
Factors

A factor of a positive whole number is a positive whole number that will divide exactly into it.

Worked Examples

1

List all the factors of 20.

Show me

The factors of 20 are:

1, 2, 4, 5, 10, 20

These are all numbers that divide exactly into 20.
2

Write the number 12 as the product of two factors in as many ways as possible.

Show me 12 = 1 × 12
12 = 4 × 3
12 = 2 × 6
12 = 6 × 2
12 = 3 × 4
12 = 12 × 1

Exercises

List the factors of these numbers.

List the factors in increasing order separated with commas.

(a)
14
(b)
27
(c)
6
(d)
15
(e)
18
(f)
25
(g)
40
(h)
100
(i)
45
(j)
50
(k)
36
(l)
28

Fill in the missing numbers.

(a)
32 = 4 × 2 ×
(b)
45 = × 3 × 5
(c)
27 = 3 × 3 ×
(d)
40 = 5 × × 2
(e)
50 = 5 × 2 ×
(f)
88 = 11 × 2 ×
(g)
66 = 2 × 3 ×
(h)
21 = × 3 × 7

A pattern of counting numbers is shown.

14, 15, 16, 17, 18, 19, 20, ...

(a)
(i)

Which of these numbers is a square number?

(ii)

Which of these numbers is a multiple of nine?

The pattern is continued.

(b)
(i)

What is the next square number?

(ii)

What is the next number that is a multiple of nine?