Exercise No. 1A

QUESTION NO. 1

Write down all the factors of each of the following:

(a) 16

Solution:

We have

16 = 1 x 16

= 2 x 8

= 4 x 4

Thus the factors of 16 are

1, 2, 4, 8, 16

(b) 28

Solution:

We have

28 = 1 x 28

= 2 x 14

= 4 x 7

Thus the factors of 28 are

1, 2, 4, 7, 14, 28

(c) 96

Solution:

We have

96 = 1 x 96

= 2 x 48

= 3 x 32

= 4 x 24

= 6 x 16

= 8 x 12

Thus the factors of 96 are

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

(d) 100

Solution:

We have

100 = 1 x 100

= 2 x 50

= 4 x 25

= 5 x 20

= 10 x 10

Thus the factors of 100 are

1, 2, 4, 5, 10, 20, 25, 50, 100

(e) 120

We have

120 = 1 x 120

= 2 x 60

= 3 x 40

= 4 x 30

= 5 x 24

= 6 x 20

= 8 x 15

= 12 x 10

Thus the factors of 120 are

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

(f) 210

Solution:

We have

210 = 1 x 210

= 2 x 105

= 3 x 70

= 5 x 42

= 6 x 35

= 7 x 30

= 10 x 21

= 14 x 15

Thus the factors of 210 are

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

QUESTION NO. 2

Write down the first six multiplies of the following
numbers.

(a) 4

Solution:

By multiplying 4 with

l, 2, 3, 4, 5, 6, we obtain

The six multiples of 4 i.e.

4, 8, 12, 16, 20, 24

(b) 7

Solution:

By multiplying 7 with

1, 2, 3, 4, 5, 6, we obtain

The six multiples of 7 i.e.

7, 14, 21, 28, 35, 42

(c) 9

Solution:

By multiplying 9 with

l, 2, 3, 4, 5, 6, we obtain

The six multiples of 9 i.e.

9, 18, 27, 36, 45, 54

(d) 12

By multiplying 12 with

l, 2, 3, 4, 5, 6, we obtain

The six multiples of 12 i.e.

12, 24, 36, 48, 60, 72

(e) 17

Solution:

By multiplying 17 wit

1, 2, 3, 4, 5, 6, we obtain

The six multiples of 17 i.e.

17, 34, 51, 68, 85, 102

(f) 21

Solution:

By multiplying 21 with

1, 2, 3, 4, 5, 6, we obtain

The six multiples of 21 i.e.

21, 42, 63, 84, 105, 126

QUESTION NO. 3

Circle the number that have 18 as a factor.

54, 126, 198, 240, 320.

Solution:

We have

18 x 3 = 54 

18 x 6 = 126

18 x 11 = 198

So factors of 18 are  54, 126, 198

QUESTION NO. 4

Underline the numbers which are factors of 144

1, 2, 3, 8, 9, 12, 14, 16, 32, 48, 144

Solution:

The factors of 144 are

1, 2, 3, 8, 9, 12, 16, 48, 144

QUESTION NO. 5

Identify the multiples of 8 from the following numbers.

14, 24, 32, 54, 56, 36, 72, 30, 64, 18, 40, 78, 96, 108, 120

Solution:

By multiplying 8 with

3, 4, 7, 8, 9, 5, 12, 15

We obtain the multiples of 8 from above list i.e.

24, 32, 56, 72, 64, 40, 96, 120

QUESTION NO. 6

State the numbers that have 224 as a multiple in the following:

3, 4, 12, 24, 28, 32, 36, 56

Solution:

We have

224= 4 x 56  = 14 x 16

= 28 x 8  = 32 x 7

So, the number that have 224 as a multiple from the above list are

4, 46, 28, 32, 56

QUESTION NO. 7

Use a calculator to find all the factors of the following numbers.

(a) 480

Solution:

We have

480 = 1 x 480  =2 x 240

= 3 x 160  =4 x 120

= 5 x 96  = 6 x 80

= 8 x 60  = 10 x 48

= 12 x 40  = 15 x 32

= 16 x 30  = 20 x 24

So the factors of 480 are

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480

(b) 600

Solution:

We have

600 = 1 x 600  = 2 x 300

= 3 x 200  = 4 x 150

= 5 x 120  = 6 x 100

= 8 x 75  = 10 x 60

= 12 x 50  = 15 x 40

= 20 x 30  = 24 x 25

So the factors of 600 are

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600

(c) 960

Solution:

We have

960 = 1 x 960  = 2 x 480

= 3 x 320  = 4 x 240

= 5 x 192  = 6 x 160

= 8 x 120  = 10 x 96

= 12 x 80  = 15 x 64

= 16 x 60 = 20 x 48

= 24 x 40  = 30 x 32

so, the factors of 960 are

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 240, 320, 480, 960

(d) 936

Solution:

We have

936 = l x 936  =2 x 468

= 3 x 312  = 4 x 234

= 6 x 156  = 8 x 117

= 9 x 104  = 12 x 78

= 18 x 52  = 24 x 39

= 26 x 36

So the factors of 936 are

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 26, 36, 39, 52, 78, 104, 117, 156, 234, 312, 468, 936

QUESTION NO. 8

John has 48 orange-flavoured sweets and Susan has 45 lime-flavoured sweets.

(a) John wishes to divide his sweets equally into bags. List all the possible ways he can do this. (For Example, he can have 6 bags of 8 sweets)

Solution:

He can have

1 bags 48 Sweets

2 bags 24 Sweets

3 bags  16 Sweets

4 bags 12 Sweets

6 bags  8 Sweets

8 bags   6 Sweets

12 bags 4 Sweets

16 bags 3 Sweets

24 bags 2 Sweets

48 bags 1 Sweets

(b) Susan also wishes to divide her sweets equally into
bags. List all the possible ways she can do this.

She can have

1 bag 45 Sweets

3 bags 15 Sweets

5 bags 9 Sweets

9 bags 5 Sweets

15 bags 3 Sweets

45 bags l Sweets

(c) Peter, their good friend, suggests that they combine
the sweets and divide them equally into bugs in such a way that each bag has equal number of orange flavoured and lime-flavoured sweets. Explain how
this can be done.

Solution:

3 bags each contain 16 orange flavoured gums and 15 lime flavoured gums

QUESTION NO. 9

Determine whether each of the following is a prime number or a composite number.

(a) 2

Solution:

2 is prime number because it is divisible by 1 and by itself only.

(b) 15

Solution:

15 is composite number because it is divisible by 1, 3, 5, 15

(c) 17

Solution:

17 is prime number because it is divisible by l and by itself only.

(d) 21

Solution:

21 is composite number because it is divisible on

1, 3, 7, 21

(e) 27

Solution:

27 is composite number which is divisible on 1, 3, 9, 27

(f) 29

Solution:

29 is prime number because which is divisible on 1 and by itself only.

QUESTION NO. 10

Name the next five prime numbers after 30.

Solution:

Five prime numbers after 30 are 31, 37, 41, 43, 47

QUESTION NO. 11

Find two prime number whose sum is an odd number. Must one of the numbers be 2?

Solution:

1st prime number = 2

Let second prime number = x

Result = Odd Number

This could be

2 + 3 = 5

3 is the second prime number

5 is the result and odd number 2, 3 or 2, 5 or 7, 9

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