Factors · Factors · 1.2

Find all factors.

To find every factor, look for factor pairs — two numbers that multiply to give the number. For 24: 1×24, 2×12, 3×8, 4×6. Collect both numbers from each pair.

01 / THE IDEA

See it work.

Watch the method

Find all factors

24 = 1×24 = 2×12 = 3×8 = 4×6.

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2424
1

Find the factor pairs

Look for pairs that multiply to 24.

1×24,  2×12,  3×8,  4×61 \times 24,\; 2 \times 12,\; 3 \times 8,\; 4 \times 6
2

List every factor

Collect both numbers from each pair, in order.

1,2,3,4,6,8,12,241, 2, 3, 4, 6, 8, 12, 24
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.

Pairs that multiply

Work up from 1; each divisor gives a partner. Stop when the pair starts to repeat.

Why it works

4×6 and 6×4 are the same pair.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

List all the factors of 48.

1

Find the factor pairs

Look for pairs that multiply to 48. 1 × 48, 2 × 24, 3 × 16, 4 × 12, 6 × 8

2

List every factor

Collect both numbers from each pair, in order. 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

EX 2medium

List all the factors of 48.

1

Find the factor pairs

Look for pairs that multiply to 48. 1 × 48, 2 × 24, 3 × 16, 4 × 12, 6 × 8

2

List every factor

Collect both numbers from each pair, in order. 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

EX 3hard

List all the factors of 20.

1

Find the factor pairs

Look for pairs that multiply to 20. 1 × 20, 2 × 10, 4 × 5

2

List every factor

Collect both numbers from each pair, in order. 1, 2, 4, 5, 10, 20

04 / COMMON TRAPS

Where students slip.

Trap

Missing a factor pair.

Fix

Check every number up to the square root.

Trap

Listing a pair twice.

Fix

Stop when pairs repeat (past the square root).

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 36.

Need a hint?
  • Find pairs that multiply to the number.
  • Collect both numbers from each pair.
C2

List all the factors of 18.

Need a hint?
  • Find pairs that multiply to the number.
  • Collect both numbers from each pair.
C3

List all the factors of 16.

Need a hint?
  • Find pairs that multiply to the number.
  • Collect both numbers from each pair.
C4

List all the factors of 18.

Need a hint?
  • Find pairs that multiply to the number.
  • Collect both numbers from each pair.
Apply

Apply (4)

A1

List all the factors of 28.

Need a hint?
  • Find pairs that multiply to the number.
  • Collect both numbers from each pair.
A2

List all the factors of 28.

Need a hint?
  • Find pairs that multiply to the number.
  • Collect both numbers from each pair.
A3

List all the factors of 16.

Need a hint?
  • Find pairs that multiply to the number.
  • Collect both numbers from each pair.
A4

List all the factors of 16.

Need a hint?
  • Find pairs that multiply to the number.
  • Collect both numbers from each pair.
Extension

Extension (4)

E1

List all the factors of 48.

Need a hint?
  • Find pairs that multiply to the number.
  • Collect both numbers from each pair.
E2

List all the factors of 24.

Need a hint?
  • Find pairs that multiply to the number.
  • Collect both numbers from each pair.
E3

List all the factors of 36.

Need a hint?
  • Find pairs that multiply to the number.
  • Collect both numbers from each pair.
E4

List all the factors of 24.

Need a hint?
  • Find pairs that multiply to the number.
  • Collect both numbers from each pair.