EXERCISE 3.6

1). Find the HCF of the following numbers:
a) 18, 48
Ans. 18 = 2 x 3 x 3
48 = 2 x 2 x 2 x 2 x 3
∴HCF = 2 x 3 = 6
b) 30, 42
Ans. 30 = 2 x 3 x 5
42 = 2 x 3 x 7
∴HCF = 2 x 3 = 6
c) 18, 60
Ans. 18 = 2 x 3 x 3
60 = 2 x 2 x 3 x 5
∴HCF = 2 x 3 = 5
d) 27, 63
Ans. 27 = 3 x 3 x 3
63 = 3 x 3 x 7
∴HCF = 3 x 3 = 9
e) 36, 84
Ans. 36 = 2 x 2 x 3 x 3
84 = 2 x 2 x 3 x 7
∴HCF = 2 x 2 x 3 = 12
f) 34, 102
Ans. 34 = 2 x 17
102 = 2 x 3 x 17
∴HCF = 2 x 17 = 34
g) 70, 105, 175
Ans.70 = 2 x 5 x 7
105 = 3 x 5 x 7
175 = 5 x 5 x 7
∴HCF = 5 x 7 = 35
h) 91, 112, 49
Ans.91 = 7 x 13
112 = 2 x 2 x 2 x 2 x 7
49 = 7 x 7
∴HCF = 7
i) 18, 54, 81
Ans. 18 = 2 x 3 x 3
54 = 2 x 3 x 3 x 3
81 = 3 x 3 x 3 x 3
∴HCF = 3 x 3 = 9
j) 12, 45, 75
Ans. 12 = 2 x 2 x 3
45 = 3 x 3 x 5
75 = 3 x 5 x 5
∴HCF = 3

2). What is the HCF of two consecutive Numbers?
Ans. 1
Eg: The HCF of 2 and 3 is 1
Even numbers?
Ans.2
Eg: HCF of 2 and 4 is 2
Odd numbers?
Ans.1
Eg: HCF of 3 and 5 is 1

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 factors, so HCF of 4 and 15 is 0. Is the answer correct ? If not, what is the correct HCF
Ans. No. The correct HCF is 1