## MP Board Class 6th Maths Solutions Chapter 3 Playing With Numbers Ex 3.6

Question 1.
Find the HCF of the following numbers :
(a) 18, 48
(c) 18, 60
(e) 36, 84
(g) 70, 105, 175
(i) 18,54,81
Solution:
(a) The prime factorisation of 18 and
48 are; 18 = 2 × 3 × 3
48 = 2 × 2 × 2 × 2 × 3
∴ HCF (18, 48) = 2 × 3 = 6

(b) The prime factorisation of 30 and 42 are; 30 = 2 × 3 × 5
42 = 2 × 3 × 7
∴ HCF (30, 42) = 2 * 3 = 6

(c) The prime factorisation of 18 and 60 are; 18 = 2 × 3 × 3
60 = 2 × 2 × 3 × 5
∴ HCF (18, 60) = 2 × 3 = 6

(d) The prime factorisation of 27 and 63 are; 27 = 3 × 3 × 3
63 = 3 × 3 × 7
HCF (27, 63) = 3 × 3 = 9

(e) The prime factorisation of 36 and 84 are; 36 = 2 × 2 × 3 × 3
84 = 2 × 2 × 3 × 7
HCF (36, 84) = 2 × 2 × 3 = 12

(f) The prime factorisation of 34 and 102 are; 34 = 2 × 17
102 = 2 × 3 × 17
HCF (34, 102) = 2 × 17 = 34

(g) The prime factorisation of 70, 105 and 175 are; 70 = 2 × 5 × 7
105 = 3 × 5 × 7
175 = 5 × 5 × 7
HCF (70, 105, 175) = 5 × 7 = 35

(h) The prime factorisation of 91, 112 and 49 are; 91 = 7 × 13
112 = 2 × 2 × 2 × 2 × 7
49 = 7 × 7
∴ HCF (91, 112, 49) = 7

(i) The prime factorisation of 18, 54 and 81 are; 18 = 2 × 3 × 3
54 = 2 × 3 × 3 × 3
81 = 3 × 3 × 3 × 3
HCF (18, 54, 81) = 3 × 3 = 9

(j) The prime factorisation of 12, 45 and 75 are; 12 = 2 × 2 × 3
45 = 3 × 3 × 5
75 = 3 × 5 × 5
∴ HCF (12, 45, 75) = 3 Question 2.
What is the HCF of two consecutive
(a) numbers?
(b) even numbers?
(c) odd numbers?
Solution:
(a) HCF of two consecutive numbers is 1.
(b) HCF of two consecutive even numbers is 2.
(c) HCF of two consecutive odd numbers is 1. Question 3.
HCF of co-prime numbers 4 and 15 was found as follows by factorisation :
4 = 2 × 2 and 15 = 3 × 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:
No. The correct HCF of 4 and 15 is 1.