5 Multiplication,

multiples and factors

5.1 Tables, multiples and factors
Worked example 1

Write the missing factors of 20.

Factors of 20 = 1, , , , , 20

Here is a factor bug.

1 20 Tip
2 10
20 Instead of a factor
4 5 bug you could draw
different rectangles
It is important to find all the factors of a number, using 20 squares.
so you need to be systematic. The factors are the
You can write the factors of 20 on the factor bug’s legs: lengths and widths.
• Start with 1. 1 × 20 = 20
• Try 2. 2 × 10 = 20
• Try 3. 20 ÷ 3 leaves a remainder so 3 is not a factor of 20
• Try 4. 4 × 5 = 20
• There are no more numbers to try as you have already included 5.
Answer: Factors of 20 = 1, 2, 4, 5, 10, 20

array factor inverse operations multiple product

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 5.1 Tables, multiples and factors

Exercise 5.1
Focus
1 On the hundred square:
• colour all the multiples of 2 in one colour
• colour all the multiples of 5 in a different colour.
• colour all the multiples of 7 in a different colour.
What do you notice about the multiples of 10?

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

2 Write the missing numbers in this multiplication grid.

× 3 5

2 6 8 10

4 12 16

18 30

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 5 Multiplication, multiples and factors

3 Complete this cross number puzzle.

1 2 3

4 5

6 7

8 9

ACROSS DOWN
1. 6 × 8 1. 6×7
2. 9 × 9 3. 3×6
4. 24 ÷ 6 6. 6×6
5. 63 ÷ 7 7. 8×3
8. 10 × 6
9. 7 × 2

4 The factor pairs of 8 are:

1    and    8

2    and    4

Write all the factor pairs of 18.

1    and   

2    and   

   and   

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 5.1 Tables, multiples and factors

5 Complete the factor bugs for 36 and 45.

1 36

36 45

Practice
6 The number in each brick is the product of the two numbers below it.

2 3

Write the missing numbers in these diagrams.

5 3 2 6 5 7

42

7 9 4 6 8

7 Use these signs: = < >

Write the correct sign in each box.

a 3×8 5×5 b 6×4 4×6

c 7×8 6×9 d 4×4 2×8

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 5 Multiplication, multiples and factors

8 Circle all the numbers that are not multiples of 7.

7 17 27 37 47 57 67 77 87 97
9 Shade any multiples of 7 on this grid.

37 38 39

47 48 49

57 58 59

10 Here is a hexagon maze.

You need to go from the centre to one of the outside hexagons in two steps.

1 11 6

5 2 13 17

25 10 Start 14 3

16 9 18 15

4 20 7

• Start in the centre.

• The next hexagon must be a multiple of 2.
• The next hexagon must be a multiple of 5.
What are all the possible paths you could take?

11 Circle all the factors of 12.

1 2 3 4 6 8 12 24 36 72

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 5.1 Tables, multiples and factors

Challenge
12 Complete these multiplication triangles.
The product of the two circles on each line is the number in the square.

5 5

6 24 4 7 9

28 20

7 21 4 9

13 Complete the multiplication grids.

× 3 7 9 4 2 × 3 10

5 9

12 25

6 49

16 6 36

8 100

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 5 Multiplication, multiples and factors

14 Here are four digit cards.

2 3 4 9

Use each card once to make a total that is a multiple of 7.

15 Cross out two numbers so that the sum of the remaining numbers in each row
and column is a multiple of 5.

1 2 4 8

5 6 2 3

7 7 1 3

2 6 3 9

16 Saira is thinking of two different numbers.

They are both factors of 12.

The difference between the
two numbers is 4.

What are Saira’s numbers?

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 5.2 Multiplication

5.2 Multiplication
Worked example 2
associative law carry
Calculate 345 × 9.

Estimate: Estimate first by rounding

The answer will be less than 350 × 10 = 3500 345 to 350 and 9 to 10.

Grid method: Decompose 345 into

hundreds, tens and ones.
× 300 40 5
Multiply 300 by 9, 40 by 9
and 5 by 9.
9 2700 360 45
Add the products to give
the answer.
2700 + 360 + 45 = 3105

Answer: 3105
Tip

You can use the same methods for multiplying

3-digit numbers by 1-digit numbers as you did for
multiplying 2-digit numbers by 1-digit numbers.

Exercise 5.2
Focus
1 Complete this calculation.

6 × 15 = 6 × 5 × 3

= ×3

= 90

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 5 Multiplication, multiples and factors

2 The numbers in the circles are multiplied together to give the numbers
in the squares between them. Fill in the missing numbers.

13 34

3 5 2 7

14 5

3 4 21 3

3 What is double 78?

4 Find the product of 58 and 9.

5 Here are some number cards.

1 2 3 12 18 36

Use each card once to make three products with the same answer.

× = × =

× =

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 5.2 Multiplication

Practice
6 a Emma and Astrid calculate 9 × 2 × 5.
Complete their calculations. Who chose the better method?
Emma’s method Astrid’s method

9×2×5 9×2×5

= × = ×

= =

b Mario and Ian calculate 2 × 5 × 7.

Complete their calculations. Who chose the better method?
Mario’s method Ian’s method

2×5×7 2×5×7

= × = ×

= =

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 5 Multiplication, multiples and factors

7 Work out these calculations. Show your methods.

Remember to estimate first.
a 25 × 8 b 69 × 6 c 76 × 9

8 Circle all the products equal to 2400.

900 × 3     300 × 8     600 × 4

300 × 7     400 × 6     800 × 3

9 Pierre uses the grid method to work out his calculations, but then spills
ink on his work. What numbers are under the ink blots?
147 × 3 =

× 100 40 7
=
3 300 21 21

10 Write what the missing digits could be.

× = 750

How many different answers can you find?

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 5.2 Multiplication

Challenge
11 Amy and Heidi work out 6 × 15.
Amy’s method Heidi’s method

6 × 15 = 6 × 5 × 3 6 × 15 = 3 × 2 × 15

= 30 × 3 = 3 × 30
= 90 = 90

Which method do you like best?

Explain why.
Write two other methods for calculating 6 × 15.

12 Estimate the following first, then calculate. Show your working.

a 318 × 2 b 426 × 3 c 512 × 7

13 Adah is thinking of a number. She divides the number by 3 and her answer is 234.

What number is Adah thinking of?

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 5 Multiplication, multiples and factors

14 Write the same digit in each box to make the calculation correct.

3 6

3 5 6 4

15 Use the digits 3, 6, 7 and 8 to make the largest product.

× =

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