36 + 8 can be written as 4 × (9 + 2), because 4 divides both.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Use the greatest one
2 also divides both, giving 2 × (18 + 4). Using the greatest common factor leaves the smallest numbers inside.
What goes inside
Divide each original number by the factor: 36 ÷ 4 = 9 and 8 ÷ 4 = 2.
Check by expanding
4 × 9 is 36 and 4 × 2 is 8. Multiply back out and the original sum returns.
The distributive property, backwards
You know 3 × (4 + 5) = 3 × 4 + 3 × 5. Read right to left: 12 + 15 = 3 × (4 + 5). Pulling out a common factor is the same property used in the other direction, and it is the foundation of factorising in algebra.
Pull out the greatest common factor
For 18 + 24, the GCF is 6, so it becomes 6 × (3 + 4). Pulling out a smaller common factor like 2 also works — 2 × (9 + 12) — but leaves more to do. Taking the greatest one finishes the job in a single step.
Check by expanding back
6 × (3 + 4) = 18 + 24. Multiplying back out should return exactly what you started with. If it does not, the factor was applied to only one term — the commonest slip when factorising.
Why bother
Factored form often reveals structure: 18 + 24 being 6 × 7 tells you the total is a multiple of 6. In algebra, factorising is how equations get solved. Meeting it here with plain numbers means the algebra later will feel familiar.
Step 2: Try It Yourself
Tap and try it out.
9 + 9 + 9 + 9 = 36
4 × 9 = 36
4 rows of 9 makes 36.
Step 3: Watch an Example
One step at a time.
Watch Leo Factor 24 + 18
Leo rewrites 24 + 18 with a common factor outside.
- Step 1
He lists what divides 24: 1, 2, 3, 4, 6, 8, 12, 24.
Step 4: Your Turn
Practice makes it stick.
The Common Factor
Problem 1 of 2
What is the greatest common factor of 20 and 30?
Inside the Bracket
Problem 2 of 2
20 + 30 = 10 × (2 + ?). What goes in place of the question mark?
Take the Factor Out
1 of 4
Greatest common factor of 12 and 18?
2 of 4
12 + 18 = 6 × (2 + ?). What is the missing number?
3 of 4
Greatest common factor of 15 and 25?
4 of 4
15 + 25 = 5 × (3 + ?). What is the missing number?
Step 5: Quick Check
Show what you know.
Question 1 of 1
Greatest common factor of 16 and 24?
What You Learned
- A sum can be rewritten as a common factor times a smaller sum.
- Divide each number by the factor to find what goes in the bracket.
- Using the greatest common factor leaves the smallest numbers inside.