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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
(a) 18, 48
18 = 2 × 3 × 3
48 = 2 × 2 × 2 × 2 × 3
HCF = 2 × 3 = 6
(b) 30, 42
30 = 2 × 3 × 5
42 = 2 × 3 × 7
HCF = 2 × 3 = 6
(c) 18, 60
18 = 2 × 3 × 3
60 = 2 × 2 × 3 × 5
HCF = 2 × 3 = 6
(d) 27, 63
27 = 3 × 3 × 3
63 = 3 × 3 × 7
HCF = 3 × 3 = 9
(e) 36, 84
36 = 2 × 2 × 3 × 3
84 = 2 × 2 × 3 × 7
HCF = 2 × 2 × 3 = 12
(f) 34, 102
34 = 2 × 17
102 = 2 × 3 × 17
HCF = 2 ×17 = 34
(g) 70, 105, 175
70 = 2 × 5 × 7
105 = 3 × 5 × 7
175 = 5 × 5 × 7
HCF = 5 × 7 = 35
(h) 91, 112, 49
91 = 7 × 13
112 = 2 × 2 × 2 × 2 × 7
49 = 7 × 7
HCF = 7
(i) 18, 54, 81
18 = 2 × 3 × 3
54 = 2 × 3 × 3 × 3
81 = 3 × 3 × 3 × 3
HCF = 3 × 3 = 9
(j) 12, 45, 75
12 = 2 ×2 × 3
45 = 3 × 3 × 5
75 = 3 × 5 × 5
HCF = 3
What is the HCF of two consecutive
(a) Numbers? (b) Even numbers? (c) Odd numbers?
(i) 1 e.g., HCF of 2 and 3 is 1.
(ii) 2 e.g., HCF of 2 and 4 is 2.
(iii) 1 e.g., HCF of 3 and 5 is 1.
HCF of co-prime numbers 4 and 15 was found as follows by factorization:
4 = 2 × 2 and 15 = 3 × 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?
No. The answer is not correct. 1 is the correct HCF.
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