Year 5 Use common factors and multiples to solve calculations efficiently worksheet

“Numbers that share” is free to print, with no account. It is the first sheet in the Year 5 maths unit “Use common factors and multiples to solve calculations efficiently”, for children aged 9 to 10, and takes about 20 minutes.

Print it on A4. The child's pages come first; the answers, and what each wrong answer tells you, are on the grown-up page that follows. Week 24 of the year, 5 sheets in the unit.

Free sample · answers on the last page

Numbers that share

Name: ____________ · Date: ____________
Year 5 · Maths · about 20 minutes
Answers are on the grown-up page

Today I can find the factors that two numbers share, and the highest common factor.

A Look back3 min

1.
6 × 4 =
2.
Write the prime numbers from 10 to 20.
3.
24 counters are shared equally into 4 groups. Each group has counters.

B Watch me, then you4 min

Find every factor of 12. Make rectangles with 12 counters.

Watch me

12 counters make 3 rows of 4, so 3 and 4 are factors.

They also make 2 rows of 6, so 2 and 6 are factors.

1 and 12 always work too.

Now you

1.
List all the factors of 10.

C Your turn5 min

1.
Write every common factor of 6 and 9.
2.
Write every common factor of 8 and 12.
3.
Write every common factor of 10 and 15.
4.
What is the highest common factor of 12 and 16?

Say it out loud: Why is 1 always on the list of common factors? Can you find two numbers where 1 is the highest common factor?

D Spot the mistake3 min

Sam says: “24 and 36 share one 2 and one 3, so their highest common factor is 2 × 3 = 6.”

1.
What is the highest common factor of 24 and 36?

E Think deeper4 min

1.
Kit has 24 red counters and 36 blue counters. Each group holds one colour. All groups are the same size, with none left over. What is the biggest group size?

How did it feel?

I can do it Nearly Not yet

For the grown-up

Numbers that share · 2 minutes to read

Answers, and what a wrong one tells you

A

1. 24

2. 11, 13, 17, 19

3. 6

B

1. 1, 2, 5, 10

C

1. 1, 3 If your child includes a number that divides only one of the two, test it against both numbers in turn.

2. 1, 2, 4 If your child leaves a factor out, test each factor of 8 against 12 in turn.

3. 1, 5

4. 4 If your child writes a common factor that is too small, look for the biggest number that is in both factor lists.

D

1. 12 If your child writes 6, they have used 2 × 3 and missed a 2. 24 has three 2s and 36 has two 2s, so they share two 2s. Circle both shared 2s, then multiply.

E

1. 12 counters in each group. 24 ÷ 12 = 2 red groups and 36 ÷ 12 = 3 blue groups. If your child writes 6, groups of 6 do fit both colours, but they are not the biggest. Ask whether 12 also fits 24 and 36.

Words to use

Say“Which numbers divide into both? Which one is the biggest?”

Instead of“Just tell them the answer and move on.”

After the sheet

Lay out 24 buttons and 36 buttons. Try making rows of the same length from each pile with none left over, then find the longest row that works for both.

Tick what your child got right in StudyDen. Anything missed comes back in a later Look back box, so there's no need to redo the sheet.

The rest of this unit

4 more sheets come with a StudyDen plan, in teaching order:

Shared times table numbers(with a plan)
Sorting numbers by properties(with a plan)
Factor pairs of 100(with a plan)
Friendlier numbers to multiply(with a plan)

Every Year 5 maths worksheet

The worksheets plan opens a printable sheet for every lesson in Years 1 to 6, each with its answers on a separate page for you. It costs £6.99 a month or £59 a year for the whole family, with no free trial.

The full StudyDen plan adds the lessons themselves, marked as your child works, with the worksheets included. It is 7 days free, then £29.99 a month.

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