Factors · Greatest common factor · 4.1

Common factors.

A common factor divides both numbers. 12 and 18 share the factors 1, 2, 3, and 6. The greatest of these — 6 — is the greatest common factor (GCF).

01 / THE IDEA

See it work.

Watch the method

Common factors

12 and 18 share 1, 2, 3, 6 — the GCF is 6.

1 / 2
gcd⁡(12, 18)\gcd(12,\, 18)
1

List the factors of each

Factors of 12 and of 18.

1,2,3,4,6,12  ∣  1,2,3,6,9,181, 2, 3, 4, 6, 12\;\mid\; 1, 2, 3, 6, 9, 18
2

The greatest common one

The biggest factor they share is the GCF.

gcd⁡(12,18)=6\gcd(12,18) = 6
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 6.

streak 0
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— / WHY IT WORKS

The idea underneath.

Shared factors

List the factors of each number; the ones in both are common factors, and the largest is the GCF.

Why it works

6 divides both 12 and 18.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Find the GCF of 18 and 42.

1

List the factors of each

Factors of 18 and of 42. 1, 2, 3, 6, 9, 18 | 1, 2, 3, 6, 7, 14, 21, 42

2

The greatest common one

The biggest factor they share is the GCF. gcd(18,42) = 6

EX 2medium

Find the GCF of 16 and 12.

1

List the factors of each

Factors of 16 and of 12. 1, 2, 4, 8, 16 | 1, 2, 3, 4, 6, 12

2

The greatest common one

The biggest factor they share is the GCF. gcd(16,12) = 4

EX 3hard

Find the GCF of 30 and 18.

1

List the factors of each

Factors of 30 and of 18. 1, 2, 3, 5, 6, 10, 15, 30 | 1, 2, 3, 6, 9, 18

2

The greatest common one

The biggest factor they share is the GCF. gcd(30,18) = 6

04 / COMMON TRAPS

Where students slip.

Trap

Picking a factor of only one number.

Fix

A common factor must divide BOTH.

Trap

Taking a small common factor.

Fix

The GCF is the GREATEST common one.

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

Find the GCF of 8 and 28.

Need a hint?
  • Find the factors of each.
  • The biggest shared factor is the GCF.
C2

Find the GCF of 12 and 30.

Need a hint?
  • Find the factors of each.
  • The biggest shared factor is the GCF.
C3

Find the GCF of 6 and 6.

Need a hint?
  • Find the factors of each.
  • The biggest shared factor is the GCF.
C4

Find the GCF of 10 and 6.

Need a hint?
  • Find the factors of each.
  • The biggest shared factor is the GCF.
Apply

Apply (4)

A1

Find the GCF of 9 and 15.

Need a hint?
  • Find the factors of each.
  • The biggest shared factor is the GCF.
A2

Find the GCF of 6 and 14.

Need a hint?
  • Find the factors of each.
  • The biggest shared factor is the GCF.
A3

Find the GCF of 8 and 12.

Need a hint?
  • Find the factors of each.
  • The biggest shared factor is the GCF.
A4

Find the GCF of 8 and 12.

Need a hint?
  • Find the factors of each.
  • The biggest shared factor is the GCF.
Extension

Extension (4)

E1

Find the GCF of 15 and 21.

Need a hint?
  • Find the factors of each.
  • The biggest shared factor is the GCF.
E2

Find the GCF of 8 and 6.

Need a hint?
  • Find the factors of each.
  • The biggest shared factor is the GCF.
E3

Find the GCF of 4 and 6.

Need a hint?
  • Find the factors of each.
  • The biggest shared factor is the GCF.
E4

Find the GCF of 4 and 14.

Need a hint?
  • Find the factors of each.
  • The biggest shared factor is the GCF.