Chapter 8 - Multiples and Factors
Practice Set 32
Write the factors of the following numbers.
(1) 8
Solution:
Factors of 8 – 1, 2, 4, 8
(2) 5
Solution:
Factors of 5 – 1, 5
(3) 14
Solution:
Factors of 14 – 1, 2, 7, 14
(4) 10
Solution:
Factors of 10 – 1, 2, 5, 10
(5) 7
Solution:
Factors of 7 – 1, 7
(6) 22
Solution:
Factors of 22 – 1, 2, 11, 22
(7) 25
Solution:
Factors of 25 – 1, 5, 25
(8) 32
Solution:
Factors of 32 – 1, 2, 4, 8, 16, 32
(9) 33
Solution:
Factors of 33 – 1, 3, 11, 33
Practice Set 33
1. (1) Write five three-digit numbers that are multiples of 2.
Solution:
Five three-digit numbers that are multiples of 2 are;
(i) 124
(ii) 280
(iii) 552
(iv) 786
(v) 928
(2) Write five three-digit numbers that are multiples of 5.
Solution:
Five three-digit numbers that are multiples of 5 are;
(i) 105
(ii) 290
(iii) 385
(iv) 470
(v) 565
(3) Write five three-digit numbers that are multiples of 10.
Solution:
Five three-digit numbers that are multiples of 5 are;
(i) 720
(ii) 300
(iii) 940
(iv) 180
(v) 760
2. Write 5 numbers that are multiples of 2 as well as of 3.
Solution:
5 numbers that are multiples of 2 as well as 3 are:
(i) 12
(ii) 30
(iii) 48
(iv) 66
(v) 90
3. A ribbon is 3 metres long. Can we cut it into 50 cm pieces and have nothing left over ? Write the reason why or why not.
Solution:
We know that
3 m = 300 cm
To know whether it can cut it into 50 cm pieces or not,
We’ll divide 300 by 50
∴ \( \frac{300}{50} \) = 6
We will get 6 equal pieces and nothing is left over.
Ans: We cut it into 50 cm pieces and have nothing left over.
4. A ribbon is 3 metres long. I need 8 pieces of ribbon each 40 cm long. How many centimetres shorter is the ribbon than the length I need?
Solution:
I need 1 piece of 40 cm
So for 8 pieces, I’ll require 40 x 8 = 320 cm of ribbon
We know that 3 m = 300 cm
But the ribbon is 300 cm long.
So the ribbon is shorter by 320 – 300 = 20 cm
Ans: The ribbon is shorter by 20 cm.
5. If the number given in the table is divisible by the given divisor, put ✓ in the box. If it is not divisible by the divisor, put 5 in the box.
Solution:
Practice Set 34
1. Write all the prime numbers between 1 and 20.
Solution:
Prime numbers between 1 and 20 are;
2, 3, 5, 7, 11, 13, 17, 19.
2. Write all the composite numbers between 21 and 50.
Solution:
Composite numbers between 21 and 50 are;
22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49.
3. Circle the prime numbers in the list given below.
22, 37, 43, 48, 53, 60, 91, 57, 59, 77, 79, 97, 100
Solution:
4. Which of the prime numbers are even numbers ?
Solution:
There is only one prime number that is also an even number, which is “2”.
Practice Set 35
Determine whether the pairs of numbers given below are co-prime numbers.
(1) 22, 24
Solution:
Factors of 22 – 1, 2, 11, 22
Factors of 24 – 1, 2, 3, 4, 6, 8, 12, 24
Common Factors – 1, 2
∴ 22 and 24 are not coprime numbers.
(2) 14, 21
Solution:
Factors of 14 – 1, 2, 7, 14
Factors of 21 – 1, 3, 7, 21
Common Factors – 1, 7
∴ 14 and 7 are not co-prime numbers.
(3) 10, 33
Solution:
Factors of 10 – 1, 2, 5, 10
Factors of 33 – 1, 3, 11, 33
Common Factor – 1
∴ 10 and 33 are coprime numbers.
(4) 11, 30
Solution:
Factors of 11 – 1, 11
Factors of 30 – 1, 2, 3, 5, 6, 10, 15, 30
Common Factor – 1
∴ 11 and 30 are coprime numbers.
(5) 5, 7
Solution:
Factors of 5 – 1, 5
Factors of 7 – 1, 7
Common Factor – 1
∴ 5 and 7 are coprime numbers.
(6) 15, 16
Solution:
Factors of 15 – 1, 3, 5, 15
Factors of 16 – 1, 2, 4, 8, 16
Common Factor – 1
∴ 15 and 16 are coprime numbers.
(7) 50, 52
Solution:
Factors of 50 – 1, 2, 5, 10, 25, 50
Factors of 52 – 1, 2, 4, 13, 26, 51
Common Factors – 1, 2
∴ 50 and 52 are not coprime numbers.
(8) 17, 18
Solution:
Factors of 17 – 1, 17
Factors of 18 – 1, 2, 3, 6, 9, 18
Common Factor – 1
∴ 17 and 18 are coprime numbers.