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Grade 6 · Maths · Lessons
The biggest factor they share
✖️factors🔢common🧩greatest➕sum
The biggest factor.
The big ideaThe greatest common factor is the biggest number that goes into both.

How it works

The greatest common factor is the biggest number that goes into both.

You can write a sum as a common factor times a sum: 20 + 8 = 4 × (5 + 2).

The common factor comes out of the brackets.

Factors of 20 and 8• both have 4• 4 is the greatestWritten as• 4 × (5 + 2)• = 28
20 + 8.

Example 1: Fill the gap

  1. 20 + 8 = 4 × (? + 2).
  2. 4 × 5 = 20 and 4 × 2 = 8, so the gap is 5.
  3. 20 + 8 = 4 × (5 + 2).

Example 2: Another

  1. 30 + 18 = 6 × (? + 3).
  2. 6 × 5 = 30 and 6 × 3 = 18, so the gap is 5.
  3. 30 + 18 = 6 × (5 + 3).

Example 3: Find the greatest factor

  1. 24 + 78.
  2. 6 goes into 24 and 78. 24 ÷ 6 = 4 and 78 ÷ 6 = 13.
  3. 24 + 78 = 6 × (4 + 13).

Words to know

common factor
A factor that two numbers share.
greatest common factor
The biggest common factor.

Watch out

Try it

  1. What is the greatest common factor of 12 and 18?
  2. Fill in: 12 + 8 = 4 × (3 + ?)
  3. Write 15 + 10 as 5 × (? + ?)
  4. Is 5 a common factor of 15 and 25?
Answers: 1. 6 · 2. 2 · 3. 5 × (3 + 2) · 4. yes
For grown-upsList factors of two numbers on paper and circle the ones they share.
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