Punjab State Board PSEB 5th Class Maths Book Solutions Chapter 3 HCF and LCM Ex 3.2 Textbook Exercise Questions and Answers.

## PSEB Solutions for Class 5 Maths Chapter 3 HCF and LCM Ex 3.2

Question 1.

Write the Prime numbers from the following :

Solution:

(a) 5, 7, 3

(b) 2, 11, 13

(c) 5

(d) 41, 23, 17, 19

(e) 41, 37, 47.

Question 2.

Write the composite numbers from the following :

Solution:

(a) 14, 9, 6

(b) 21, 12, 18

(c) 32, 15

(d) 10, 25, 9

(e) 24, 49, 50.

Question 3.

Find HCF of following numbers using Prime factorisation.

(a) 18, 27

(b) 21, 63

(c) 80, 100

(d) 42, 98.

Solution:

Prime factorisation of 18 = 2 × 3 × 3

Prime factorisation of 27 = 3 × 3 × 3

Common Prime Factors = 3 and 3

∴ HCF of 18 and 27 = 3 × 3 = 9

Prime factorisation of 21 = 3 × 7

Prime factorisation of 63 = 3 × 3 × 7

Common Prime Factors = 3 and 7

∴ HCF of 21 and 63 = 3 × 7 = 21

Prime factorisation of 80 = 2 × 2 × 2 × 2 × 5

Prime factorisation of 100 = 2 × 2 × 5 × 5

Common Prime Factors = 2, 2 and 5

HCF of 80 and 100 = 2 × 2 × 5 = 20

Prime factorisation of 42 = 2 × 3 × 7

Prime factorisation of 98 = 2 × 7 × 7

Common Prime Factors = 2 and 7

HCF of 42 and 98 = 2 × 7 = 14

Question 4.

Find HCF of following numbers using Prime factorisation :

(a) 30, 50, 70

(b) 24, 32, 40

(b) 36, 60, 72

(d) 25, 30, 35.

Solution:

Prime factorisation of 30 = 2 × 3 × 5

Prime factorisation of 50 = 2 × 5 × 5

Prime factorisation of 70 = 2 × 5 × 7

Common Prime Factors = 2 and 5

∴ HCF of 30, 50 and 70 = 2 × 5 = 10

Prime factorisation of 24 = 2 × 2 × 2 × 3

Prime factorisation of 32 = 2 × 2 × 2 × 2 × 2

Prime factorisation of 40 = 2 × 2 × 2 × 5

Common Prime Factors = 2, 2 and 2

∴ HCF of 24, 32 and 40 = 2 × 2 × 2 = 8

Prime factorisation of 36 = 2 × 2 × 3 × 3

Prime factorisation of 60 = 2 × 2 × 3 × 5

Prime factorisation of 72 = 2 × 2 × 2 × 3 × 3

Common Prime Factors = 2, 2 and 3

∴ HCF of 36, 60 and 72 = 2 × 2 × 3 = 12

Prime factorisation of 25 = 5 × 5

Prime factorisation of 30 = 2 × 3 × 5

Prime factorisation of 35 = 5 × 7

Common Prime Factor = 5

∴ HCF of 25, 30, 35 = 5

Question 5.

Find HCF of following numbers using Prime factorisation :

(a) 42, 84

(b) 45, 90

(c) 16, 64, 80

(d) 45, 90, 105.

Solution:

Prime factorisation of 42 = 2 × 3 × 7

Prime factorisation of 84 = 2 × 2 × 3 × 7

Common Prime Factors = 2, 3 and 7

∴ HCF of 42, 84 = 2 × 3 × 7 = 42

Prime factorisation of 45 = 3 × 3 × 5

Prime factorisation of 90 = 2 × 3 × 3 × 5

Common Prime Factors = 3, 3 and 5

HCF of 45, 90 = 3 × 3 × 5 = 45

Prime factorisation of 16 = 2 × 2 × 2 × 2

Prime factorisation of 64 = 2 × 2 × 2 × 2 × 2 × 2

Prime factorisation of 80 = 2 × 2 × 2 × 2 × 5

Common Prime Factors = 2, 2, 2 and 2

∴ HCF of 16, 64, 80 = 2 × 2 × 2 × 2 = 16

Prime factorisation of 45 = 3 × 3 × 5

Prime factorisation of 90 = 2 × 3 × 3 × 5

Prime factorisation of 105 = 3 × 5 × 7

Common Prime Factors = 3 and 5

∴ HCF of 45, 90 and 105 = 3 × 5 = 15

Question 6.

Find HCF of following numbers using Division method :

(a) 48, 60

(b) 120, 140

(c) 12, 18, 64

(d) 60, 96, 128

Solution:

(a)

∴ HCF of 120 and 140 = 20

(c) First find HCF of any two numbers say 12 and 18.

∴ HCF of 12, 18 and 64 = 2

(d) First find HCF of any two numbers say 60 and 96.

∴ HCF of 60 and 96 = 12

Now find HCF of 12 and 128

∴ HCF of 60, 96, 128 = 4

Question 7.

Find the largest number which divides 60, 75 and 90 without leaving any remainder.

Solution:

The largest number which divides 60, 75 and 90 without leaving any remainder = HCF of 60, 75 and 90

First find HCF of any two numbers say 60 and 75.

∴ HCF of 60 and 75 = 15

Now, find HCF of 15 and 90

The greatest number which divides 60, 75 and 90 = 15

Question 8.

There are three drums that contain 36l, 45l, and 72l milk respectively. Find the largest vessel which can measure milk of all the three drums completely.

Solution:

The capacity of the largest vessel that can measure milk of all the three drums completely = 9 l.