Factors, Multiples and Divisibility
Express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another. Create and use algorithms involving a sequence of steps and decisions and digital tools to experiment with factors, multiples and divisibility; identify, interpret and describe emerging patterns.
Read this first
A factor divides into a number exactly. A multiple is what you land on when you count up.
12 makes 3 rows of 4. So 3 and 4 are factors of 12.
Words you need
- Factor
- A number that divides in exactly.
- Multiple
- A number you land on when counting up in steps.
- Divisible
- Divides with nothing left over.
Worked example
e.g. Find all the factors of 12.
- Start at 1. Does 1 divide into 12? Yes. Its partner is 12.
- Try 2. Yes, 2 x 6 = 12. Write 2 and 6.
- Try 3. Yes, 3 x 4 = 12. Write 3 and 4.
- Try 4. You already have it. Stop.
- The factors are 1, 2, 3, 4, 6 and 12.
Work in pairs. Stop when the pairs start repeating.
Practice
The pictures fade as you go. By the last few you are on your own.
1Is 3 a factor of 12?with a picture
AnswerYes. 12 makes three equal rows.
2Is 5 a factor of 12?with a picture
AnswerNo. Twelve does not share into 5 equal groups.
3List the first five multiples of 6.with a hint
Need a hint?
Count up in sixes.
Answer6, 12, 18, 24, 30.
4Is 48 divisible by 4?with a hint
Need a hint?
Try 4 times something.
AnswerYes. 4 x 12 = 48.
5List all the factors of 18.on your own
Answer1, 2, 3, 6, 9, 18.
6How can you tell a number is divisible by 5?on your own
AnswerIt ends in 0 or 5.
7How can you tell a number is divisible by 10?on your own
AnswerIt ends in 0.
Think about it
1
What is the difference between a factor and a multiple?
One good answerFactors are smaller and divide in. Multiples are bigger and count up.
2
Why does every number have 1 as a factor?
One good answer1 divides into everything exactly once.
Common mistakes
Mixing up factors and multiples.
Factors go into it. Multiples come out of it.
Missing a factor pair.
Work up from 1 in pairs. Then none get lost.