Gujarat Board GSEB Textbook Solutions Class 6 Maths Chapter 3 Playing With Numbers Ex 3.6 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 6 Maths Chapter 3 Playing With Numbers Ex 3.6

Question 1.

Find the HCF of the following numbers:

(a) 18, 48

(b) 30, 42

(c) 18, 60

(d) 27, 63

(e) 36, 84

(f) 34, 102

(g) 70, 105, 175

(h) 91, 112, 49

(i) 18, 54, 81

(j) 12, 45, 75

Solution:

(a) 18 and 48

Factors of 18 are: 1, 2, 3, 6, 9 and 18

Factors of 48 are: 1,2, 3,4, 6, 8, 12, 16, 24 and 48

Their common factors are: 1, 2, 3 and 6

Since, the highest common factor is 6,

HCF of 18 and 48 = 6

(b) 30 and 42

Factors of 30 are: 1, 2, 3, 5, 6, 10, 15 and 30

Factors of 42 are: 1, 2, 3, 6, 7, 14, 21 and 42

Their common factors are: 1, 2, 3, 6

Since, the highest common factor is 6,

HCF of 30 and 42 = 6

(c) 18 and 60

Factors of 18 are: 1, 2, 3, 6, 9 and 18

Factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60

Their common factors are: 1, 2, 3, 6

Since, the highest common factor is 6,

HCF of 18 and 60 = 6

(d) 27 and 63

Factors of 27 are: 1, 3, 9 and 27

Factors of 63 are: 1, 3, 7, 9, 21 and 63

Their common factors are: 1, 3 and 9

Since, the highest common factor is 9,

HCF of 27 and 63 = 9

(e) 36 and 84

Factors of 36 are: 1,2,3,4,6,9, 12, 18 and 36

Factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84

Their common factors are: 1, 2, 3, 4, 6 and 12

Since, the highest common factor is 12

HCF of 36 and 84 = 12

(f) 34 and 102

Factors of 34 are: 1, 2, 17 and 34

Factors of 102 are: 1, 2, 3, 6, 17, 34, 51 and 102

Common factors are: 1, 2, 17 and 34

Since, the highest common factor is 34,

HCF of 34 and 102 = 34

(g) 70, 105 and 175

Factors of 70 are: 1, 2, 5, 7, 10, 14, 35 and 70.

Factors of 105 are: 1, 3, 5, 7, 15, 21, 35 and 105

Factors of 175 are: 1, 5, 7, 25, 35 and 175

Their common factors are: 1, 5, 7 and 35.

Since, the highest common factor is 35,

HCF of 70, 105 and 175 = 35

(h) 91, 112 and 49

Factors of 91 are: 1, 7, 13 and 91

Factors of 112 are: 1, 2, 4, 7, 8, 14, 16, 28, 56 and 112

Factors of 49 are: 1, 7 and 49

Their common factors are: 1 and 7

Since, the highest common factor = 7,

HCF of 91, 112 and 49 = 7

(i) 18, 54 and 81

Factors of 18 are: 1, 2, 3, 6, 9 and 18

Factors of 54 are: 1,2,3,6,9, 18,27 and 54

Factors of 81 are: 1, 3, 9, 27 and 81

Their common factors are: 1, 3 and 9

Since, their highest common factor is 9

HCF of 18, 54 and 81 – 9

(j) 12, 45 and 75

Factors of 12 are: 1, 2, 3, 4, 6 and 12

Factors of 45 are: 1, 3, 5, 9, 15 and 45

Factors of 75 are: 1, 3, 5, 15, 25 and 75

Their common factors are: 1 and 3

Since, the highest common factor is 3

HCF of 12, 45 and 75 = 3

Question 2.

What is the HCF of two consecutive

(a) numbers ?

(b) even numbers ?

(c) odd numbers ?

Solution:

(a) The common factor of two consecutive numbers is always 1.

HCF of two consecutive numbers = 1

(b) The common factors of two consecutive even numbers are 1 and 2.

The HCF of two consecutive even numbers = 2

(c) The common factor of two consecutive odd numbers is 1.

HCF of two consecutive odd numbers = 1

Question 3.

HCF of co-prime numbers 4 and 15 was found as follows by factorisation : 4 = 2 x 2 and 15 = 3 x 5 since there is no common prime factor, so HCF of 4 and 15 is 0. Is the answer correct ? If not, what is the correct HCF?

Solution:

cannot be a factor of any number.

1 is a factor of every number.

No common factor means, 1 is the common factor.

The given answer is incorrect. The correct

answer is: HCF of 4 and 15 = 1