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
Solutions:
(a) 18, 48
18 = 2 × 3 × 3
48 = 2 × 2 × 2 × 2 × 3
HCF = 2 × 3 = 6
Therefore, the HCF of 18, 48 is 6
(b) 30, 42
30 = 2 × 3 × 5
42 = 2 × 3 × 7
HCF = 2 × 3 = 6
Therefore, the HCF of 30, 42 is 6
(c) 18, 60
18 = 2 × 3 × 3
60 = 2 × 2 × 3 × 5
HCF = 2 × 3 = 6
Therefore, the HCF of 18, 60 is 6
(d) 27, 63
27 = 3 × 3 × 3
63 = 3 × 3 × 7
HCF = 3 × 3 = 9
Therefore, the HCF of 27, 63 is 9
(e) 36, 84
36 = 2 × 2 × 3 × 3
84 = 2 × 2 × 3 × 7
HCF = 2 × 2 × 3 = 12
Therefore, the HCF of 36, 84 is 12
(f) 34, 102
34 = 2 × 17
102 = 2 × 3 × 17
HCF = 2 × 17 = 34
Therefore, the HCF of 34, 102 is 34
(g) 70, 105, 175
70 = 2 × 5 × 7
105 = 3 × 5 × 7
175 = 5 × 5 × 7
HCF = 5 × 7 = 35
Therefore, the HCF of 70, 105, 175 is 35
(h) 91, 112, 49
91 = 7 × 13
112 = 2 × 2 × 2 × 2 × 7
49 = 7 × 7
HCF = 7
Therefore, the HCF of 91, 112, 49 is 7
(i) 18, 54, 81
18 = 2 × 3 × 3
54 = 2 × 3 × 3 × 3
81 = 3 × 3 × 3 × 3
HCF = 3 × 3 = 9
Therefore, the HCF of 18, 54, 81 is 9
(j) 12, 45, 75
12 = 2 × 2 × 3
45 = 3 × 3 × 5
75 = 3 × 5 × 5
HCF = 3
Therefore, the HCF of 12, 45, 75 is 3
2. What is the HCF of two consecutive
(a) numbers?
(b) even numbers?
(c) odd numbers?
Solutions:
(a) The HCF of two consecutive numbers is 1
Example: The HCF of 2 and 3 is 1
(b) The HCF of two consecutive even numbers is 2
Example: The HCF of 2 and 4 is 2
(c) The HCF of two consecutive odd numbers is 1
Example: The HCF of 3 and 5 is 1
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?
Solutions:
No. The answer is not correct. The correct answer is 1.
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