Year 6AC9M6N02

Factors and Multiples

Identify and describe the properties of prime, composite and square numbers and use these properties to solve problems and simplify calculations.

Read this first

A factor divides into a number exactly. A multiple is what you get when you count up in that number. They are two views of the same thing.

12 makes a neat rectangle 3 by 4, so 3 and 4 are both factors of 12. So are 1, 2, 6 and 12.

Words you need

Factor: A number that divides in exactly, with nothing left over.
Multiple: What you land on counting up in a number. Multiples of 4 are 4, 8, 12, 16 and so on.
Prime: A number with exactly two factors: 1 and itself.
Composite: A number with more than two factors.

Worked example

e.g. Find all the factors of 24.

Work in pairs, starting at 1. $1 \times 24 = 24$ , so 1 and 24 are factors.
Try 2. $2 \times 12 = 24$ , so 2 and 12 are factors.
Try 3. $3 \times 8 = 24$ , so 3 and 8 are factors.
Try 4. $4 \times 8$ is too big, but $4 \times 6 = 24$ , so 4 and 6 are factors.
Try 5. It does not divide in. Try 6, but you already have it, so stop.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

Work in pairs and go up in order. When the pairs start repeating, you have them all.

Practice

The pictures fade as you go. By the last few you are on your own.

1This rectangle shows one factor pair of 12. What is it?with a picture

Answer2 and 6, because

2 \times 6 = 12

2List all the factors of 18.with a hint

Need a hint?

Go in pairs from 1. Try 1, 2, 3 and so on.

Answer1, 2, 3, 6, 9, 18.

3Write the first five multiples of 7.with a hint

Need a hint?

Count up in sevens.

Answer7, 14, 21, 28, 35.

4List all the factors of 20.on your own

Answer1, 2, 4, 5, 10, 20.

5Is 17 prime? How do you know?on your own

AnswerYes. Nothing divides into 17 except 1 and 17, so it has exactly two factors.

6Find the highest common factor of 12 and 18.on your own

Answer6. The factors of 12 are 1, 2, 3, 4, 6, 12. The factors of 18 are 1, 2, 3, 6, 9, 18. The biggest they share is 6.

7Find the lowest common multiple of 4 and 6.on your own

Answer12. Multiples of 4 are 4, 8, 12. Multiples of 6 are 6, 12. The first one they share is 12.

8Which numbers between 20 and 30 are prime?on your own

Answer23 and 29.

Think about it

Why is 1 not a prime number?

One good answerA prime has exactly two different factors. 1 only has one factor, itself, so it does not qualify.

Every number has at least two factors. Which two, and why?

One good answer1 and the number itself, because 1 divides into everything and every number divides into itself exactly once.

How can a rectangle help you find factors?

One good answerAny rectangle you can build from that many squares gives a factor pair, since the rows and columns multiply to the total. A prime number only makes one long strip.

Why does looking for factors in pairs mean you can stop halfway?

One good answerEach factor you find hands you its partner. Once the pairs start repeating, you have found them all.

Common mistakes

Mixing up factors and multiples.

Factors are smaller and divide in. Multiples are bigger and count up. 4 is a factor of 12; 12 is a multiple of 4.

Missing factors by not working in pairs.

Go up in order from 1 and write both numbers of each pair. That way nothing gets skipped.

Calling 1 prime.

It has only one factor, not two.