Factors · Factors · 1.1

What is a factor?

A factor of a number divides it evenly, with no remainder. 3 is a factor of 12 because 12 ÷ 3 = 4 exactly. Every number has 1 and itself as factors.

01 / THE IDEA

See it work.

Watch the method

What is a factor?

3 is a factor of 12 because 12 ÷ 3 = 4.

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1212
1

Find the factor pairs

Look for pairs that multiply to 12.

1×12,  2×6,  3×41 \times 12,\; 2 \times 6,\; 3 \times 4
2

List every factor

Collect both numbers from each pair, in order.

1,2,3,4,6,121, 2, 3, 4, 6, 12
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a list, e.g. 1, 2, 3, 6.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Divides evenly

b is a factor of n if n ÷ b leaves no remainder. 1 and n itself are always factors.

Why it works

12 ÷ 4 = 3 exactly, so 4 is a factor.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

List all the factors of 18.

1

Find the factor pairs

Look for pairs that multiply to 18. 1 × 18, 2 × 9, 3 × 6

2

List every factor

Collect both numbers from each pair, in order. 1, 2, 3, 6, 9, 18

EX 2medium

List all the factors of 28.

1

Find the factor pairs

Look for pairs that multiply to 28. 1 × 28, 2 × 14, 4 × 7

2

List every factor

Collect both numbers from each pair, in order. 1, 2, 4, 7, 14, 28

EX 3hard

List all the factors of 24.

1

Find the factor pairs

Look for pairs that multiply to 24. 1 × 24, 2 × 12, 3 × 8, 4 × 6

2

List every factor

Collect both numbers from each pair, in order. 1, 2, 3, 4, 6, 8, 12, 24

04 / COMMON TRAPS

Where students slip.

Trap

Calling a multiple a factor.

Fix

A factor divides INTO the number; a multiple is built FROM it.

Trap

Forgetting 1 and the number itself.

Fix

Both are always factors.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

List all the factors of 18.

Need a hint?
  • Test which numbers divide it evenly.
  • Include 1 and the number itself.
C2

List all the factors of 28.

Need a hint?
  • Test which numbers divide it evenly.
  • Include 1 and the number itself.
C3

List all the factors of 28.

Need a hint?
  • Test which numbers divide it evenly.
  • Include 1 and the number itself.
C4

List all the factors of 36.

Need a hint?
  • Test which numbers divide it evenly.
  • Include 1 and the number itself.
Apply

Apply (4)

A1

List all the factors of 16.

Need a hint?
  • Test which numbers divide it evenly.
  • Include 1 and the number itself.
A2

List all the factors of 28.

Need a hint?
  • Test which numbers divide it evenly.
  • Include 1 and the number itself.
A3

List all the factors of 40.

Need a hint?
  • Test which numbers divide it evenly.
  • Include 1 and the number itself.
A4

List all the factors of 36.

Need a hint?
  • Test which numbers divide it evenly.
  • Include 1 and the number itself.
Extension

Extension (4)

E1

List all the factors of 20.

Need a hint?
  • Test which numbers divide it evenly.
  • Include 1 and the number itself.
E2

List all the factors of 18.

Need a hint?
  • Test which numbers divide it evenly.
  • Include 1 and the number itself.
E3

List all the factors of 24.

Need a hint?
  • Test which numbers divide it evenly.
  • Include 1 and the number itself.
E4

List all the factors of 36.

Need a hint?
  • Test which numbers divide it evenly.
  • Include 1 and the number itself.