Factors and multiples 1 I can • recognise and work out multiples of a number • recognise and work out factors of a number
Example a Write down two multiples of 16. b Write down all the factors of 16. Solution
f o o
a Multiples of 16 are 1 × 16, 2 × 16, 3 × 16, 4 × 16, and so on.
So two multiples of 16 are two from 16, 32, 48, 64, and so on. b The factors of 16 are numbers that multiply to make 16.
r p ft
16 = 1 × 16 so 1 and 16 are factors. 16 = 2 × 8 so 2 and 8 are factors. 16 = 4 × 4 so 4 is a factor.
a r D
There are no other factors of 16. There are five all together.
Practice questions 1
Write down two factors that multiply to make each boxed number.
1
a
b
c
18
2
32
21
42
Fill in the missing multiples. a Multiples of 2:
2
4
6
b Multiples of 3:
3
6
9
c Multiples of 5:
5
10
d Multiples of 10: 10 20
6
d
20
35 50
100
1
2
Circle the numbers in each row that are multiples of: a 2
4
8
10
15
18
20
21
27
35
b 3
4
8
10
15
18
20
21
27
35
c 5
4
8
10
15
18
20
21
27
35
d 10
4
8
10
15
18
20
21
27
35
Write each number as different pairs of factors. a ____ ⫻ ____
3
b
8
b 18
c 20
g 30
____ ⫻ ____
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Write down all of the factors of each number.
e 25
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____ ⫻ ____
____ ⫻ ____
a 15
4
21
d 21
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f 28 h 31
Find the common factors of both the numbers in each pair. a 15 and 24 b 18 and 24 c 10 and 25
5
Here is a list of numbers:
21
22
23
24
25
26
27
From the list, write down a all the multiples of 3
b a multiple of 6
c a multiple of 7
d a number that has 12 as a factor
e a number that has 9 as a factor
7
Factors and multiples 2 I can • work out common factors and common multiples
Example a Find all the common factors of 12 and 15. b Find two common multiples of 12 and 15. Solution a
= 1 12 12 = 2
6
12 = 3
4
15 = 1 15 15 = 3
5
f o o
The factors of 12 are 1, 2, 3, 4, 6 and 12.
r p ft
The factors of 15 are 1, 3, 5 and 15.
The common factors are factors of both numbers. They are 1 and 3.
a r D
b The multiples of 12 are 12, 24, 36, 48, 60, 72, … The multiples of 15 are 15, 30, 45, 60, 75, …
The common multiples are the numbers in both lists.
The first common multiple is 60. Further common multiples are 120, 180, 240, and so on.
Practice questions 1
a Work out the factors of 16. b Work out the factors of 28. c Write down the common factors of 16 and 28.
2
a Work out the factors of 18. b Work out the factors of 27. c Write down the common factors of 18 and 27.
8
1
a Work out the factors of 45. b Work out the factors of 63. c Write down the common factors of 45 and 63.
2
Work out the common factors of 30 and 40.
3
Work out the common factors of 50 and 75.
4
a Write down the first six multiples of 3.
f o o
b Write down the first six multiples of 5. c Work out two common multiples of 3 and 5.
5
r p ft
a Write down the first five multiples of 10.
b Write down the first five multiples of 15.
a r D
c Work out three common multiples of 10 and 15.
6
Work out two common multiples of 20 and 25.
7
Work out two common multiples of 9 and 12.
9
Mental warm-up 1: Number
Mental warm-up 2: Number
1 Round 4719 to the nearest hundred. 2 48 × 9 = 432. What is 432 ÷ 9? 3 Work out 299 + 399. 4 Work out 35 ÷ 4. 5 Tables seat five people. How many tables are needed for 27 people? 6 What is the hundreds digit in 3456? 7 The temperature is 2 °C. It falls by five degrees. What is the new temperature? 8 What fraction of this shape is filled? Write your answer as simply as possible.
1 Round 18.4 to the nearest 10. 2 13 × 15 = 195. What is 195 ÷ 13? 3 Work out 97 – 79. 4 Work out 73 ÷ 10. 5 Work out 43 + 69. 6 Write in figures six hundred and six. 7 What fraction of this shape is filled?
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3 18 3 7 10 11 2000
4 7 remainder 3 8 Down 4 degrees 12 14:15
Answers to Mental warm-up 2: Number
a r D
Write down the next number in the sequence. 11 What units should you use to measure the mass of a pen? 12 How many minutes is 212 hours? 13 Write 6.45 am in the 24-hour clock.
1 20 2 15 5 112 6 606 9 £30.05 10 101
9 Write 83 mm in centimetres. 10 Here is a sequence of numbers: 30 27 24 21 18
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8 The temperature changes from –6°C to –10°C. Has it gone up or down? How many degrees? 9 Write thirty pounds and five pence in figures. 10 Write down the next odd number after 99. 11 A bottle holds 2 litres of water. How many millilitres is that? 12 The time now is 13:45. Write down the time 30 minutes later.
243
1 4800 56 10 15
2 48 3 698 64 7 –3 °C 11 grams
4 8 remainder 3 1 84 9 8.3 cm 12 150 13 06:45
Answers to Mental warm-up 1: Number
Maths Facts
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a r D
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