Primary 4 maths · Whole numbers · About 10 minutes
Find common factors of two numbers
Match each proposed group size with the number of complete groups it makes.
Start the interactive lesson →Open practice activity
What you will learn
- Find common factors of two numbers
Models used: number sentences, stories, tables.
Before you start
Find factors that fit both numbers
We want equal group sizes that divide both 12 and 18 without leftovers.
4 rows run across the picture; each row contains 3 objects.
Twelve counters fit into four rows of three. So three is a factor of twelve.
12 ÷ 3 = 4
A factor fits exactly. Factor pairs record the two whole numbers whose product is the total.
4 rows of 3 = 4 × 3 = 12
6 rows run across the picture; each row contains 3 objects.
Eighteen counters also fit into rows of three, this time six rows. Three is a factor of both numbers.
18 ÷ 3 = 6
6 rows of 3 = 6 × 3 = 18
A common factor must fit both numbers. Read each value with the heading above its column.
List the factors of each number and keep the values in both lists. The common factors are 1, 2, 3 and 6.
Common factors: 1, 2, 3, 6
A common factor must fit both numbers Number Factors 12 1, 2, 3, 4, 6, 12 18 1, 2, 3, 6, 9, 18
What did the picture help us see?
List the factors of each number and keep the values in both lists. The common factors are 1, 2, 3 and 6.
Worked example: A new example, together
Find the greatest common factor of 30 and 12.
| Number | Some factor pairs |
|---|---|
| 30 | 1 × 30; 6 × 5 |
A product links factors and multiples. Read each value with the heading above its column.
Match each proposed group size with the number of complete groups it makes.
A factor divides a amount into complete equal groups.
A product links factors and multiples Number Some factor pairs 30 1 × 30; 6 × 5 A product links factors and multiples. Read each value with the heading above its column.
List factor pairs by testing exact division.
A product links factors and multiples Number Some factor pairs 30 1 × 30; 6 × 5 Find the greatest common factor of 30 and 12.
6
A product links factors and multiples. Read each value with the heading above its column.
List factor pairs by testing exact division.
A product links factors and multiples Number Some factor pairs 30 1 × 30; 6 × 5 A product links factors and multiples. Read each value with the heading above its column.
A common factor must divide both given numbers.
A product links factors and multiples Number Some factor pairs 30 1 × 30; 6 × 5 A product links factors and multiples. Read each value with the heading above its column.
30 ÷ 6 = 5 and 12 ÷ 6 = 2.
A product links factors and multiples Number Some factor pairs 30 1 × 30; 6 × 5 A product links factors and multiples. Read each value with the heading above its column.
Check the result against the question we started with.
30 ÷ 6 = 5 and 12 ÷ 6 = 2.
We found 6. A factor divides a amount into complete equal groups.
A product links factors and multiples Number Some factor pairs 30 1 × 30; 6 × 5
Common mistakes to discuss
- Listing the factors of one number. A common factor must divide both numbers exactly. For 12 and 18 it is 1, 2, 3 or 6.
Check your understanding
- Find common factors of two numbers
- justify a factor or common factor with exact grouping
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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