Factors · Greatest common factor · 4.2

GCF by listing.

One reliable way to find the GCF: list all factors of each number, then pick the largest one they share. For 16 (1,2,4,8,16) and 24 (1,2,3,4,6,8,12,24), the GCF is 8.

01 / THE IDEA

See it work.

Watch the method

GCF by listing

GCF(16, 24) = 8 (the largest shared factor).

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gcd⁡(16, 24)\gcd(16,\, 24)
1

List the factors of each

Factors of 16 and of 24.

1,2,4,8,16  ∣  1,2,3,4,6,8,12,241, 2, 4, 8, 16\;\mid\; 1, 2, 3, 4, 6, 8, 12, 24
2

The greatest common one

The biggest factor they share is the GCF.

gcd⁡(16,24)=8\gcd(16,24) = 8
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 6.

streak 0
best 0
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— / WHY IT WORKS

The idea underneath.

Compare the lists

Write each number’s factors, find the common ones, and choose the greatest.

Why it works

8 is the biggest factor of both 16 and 24.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Find the GCF of 24 and 42.

1

List the factors of each

Factors of 24 and of 42. 1, 2, 3, 4, 6, 8, 12, 24 | 1, 2, 3, 6, 7, 14, 21, 42

2

The greatest common one

The biggest factor they share is the GCF. gcd(24,42) = 6

EX 2medium

Find the GCF of 8 and 6.

1

List the factors of each

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

2

The greatest common one

The biggest factor they share is the GCF. gcd(8,6) = 2

EX 3hard

Find the GCF of 12 and 20.

1

List the factors of each

Factors of 12 and of 20. 1, 2, 3, 4, 6, 12 | 1, 2, 4, 5, 10, 20

2

The greatest common one

The biggest factor they share is the GCF. gcd(12,20) = 4

04 / COMMON TRAPS

Where students slip.

Trap

Missing a factor in a list.

Fix

List carefully so you don’t miss the GCF.

Trap

Stopping at the first common factor.

Fix

Keep going for the GREATEST.

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 12 and 15.

Need a hint?
  • List the factors of each number.
  • Pick the largest in both.
C2

Find the GCF of 8 and 20.

Need a hint?
  • List the factors of each number.
  • Pick the largest in both.
C3

Find the GCF of 12 and 42.

Need a hint?
  • List the factors of each number.
  • Pick the largest in both.
C4

Find the GCF of 6 and 15.

Need a hint?
  • List the factors of each number.
  • Pick the largest in both.
Apply

Apply (4)

A1

Find the GCF of 6 and 6.

Need a hint?
  • List the factors of each number.
  • Pick the largest in both.
A2

Find the GCF of 6 and 6.

Need a hint?
  • List the factors of each number.
  • Pick the largest in both.
A3

Find the GCF of 6 and 14.

Need a hint?
  • List the factors of each number.
  • Pick the largest in both.
A4

Find the GCF of 15 and 9.

Need a hint?
  • List the factors of each number.
  • Pick the largest in both.
Extension

Extension (4)

E1

Find the GCF of 12 and 18.

Need a hint?
  • List the factors of each number.
  • Pick the largest in both.
E2

Find the GCF of 12 and 42.

Need a hint?
  • List the factors of each number.
  • Pick the largest in both.
E3

Find the GCF of 6 and 10.

Need a hint?
  • List the factors of each number.
  • Pick the largest in both.
E4

Find the GCF of 6 and 6.

Need a hint?
  • List the factors of each number.
  • Pick the largest in both.