Summary of important concepts
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.