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

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

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

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.

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

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.

MP Board Class 6th Maths Solutions