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
Solution:
We will use the concept of the HCF(Highest Common Factor) to solve this.
(a) 18, 48
The prime factorizations of 18 and 48 are as follows:
18 = 2 × 3 × 3
48 = 2 × 2 × 2 × 2 × 3
The common factors, in this case, are 2 and 3.
HCF = 2 × 3 = 6
Hence, the HCF of 18, 48 is 6
(b) 30, 42
The prime factorizations of 30 and 42 are as follows:
30 = 2 × 3 × 5
42 = 2 × 3 × 7
The common factors, in this case, are 2 and 3.
HCF = 2 × 3 = 6
Hence, the HCF of 30, 42 is 6.
(c) 18, 60
The prime factorizations of 18 and 60 are as follows:
18 = 2 × 3 × 3
60 = 2 × 2 × 3 × 5
The common factors, in this case, are 2 and 3.
HCF = 2 × 3 = 6
Hence, the HCF of 18, 60 is 6.
(d) 27, 63
The prime factorizations of 27 and 63 are as follows:
27 = 3 × 3 × 3
63 = 3 × 3 × 7
The common factors, in this case, are 3 and 3.
HCF = 3 × 3 = 9
Hence, the HCF of 27, 63 is 9
(e) 36, 84
The prime factorizations of 36 and 84 are as follows:
36 = 2 × 2 × 3 × 3
84 = 2 × 2 × 3 × 7
The common factors, in this case, are 2, 2, and 3.
HCF = 2 × 2 × 3 = 12
Hence, the HCF of 36, 84 is 12
(f) 34, 102
The prime factorizations of 34 and 102 are as follows:
34 = 2 × 17
102 = 2 × 3 × 17
The common factors, in this case, are 2 and 17.
HCF = 2 × 17 = 34
Hence, the HCF of 34, 102 is 34
(g) 70, 105, 175
The prime factorizations of 70, 105, and 175 are as follows:
70 = 2 × 5 × 7
105 = 3 × 5 × 7
175 = 5 × 5 × 7
The common factors, in this case, are 5 and 7.
HCF = 5 × 7 = 35
Hence, the HCF of 70, 105, 175 is 35
(h) 91, 112, 49
The prime factorizations of 91, 112, and 49 are as follows:
91 = 7 × 13
112 = 2 × 2 × 2 × 2 × 7
49 = 7 × 7
The common factors, in this case, are 7.
HCF = 7
Hence, the HCF of 91, 112, 49 is 7
(i) 18, 54, 81
The prime factorizations of 18, 54, and 81 are as follows:
18 = 2 × 3 × 3
54 = 2 × 3 × 3 × 3
81 = 3 × 3 × 3 × 3
The common factors, in this case, are 3 and 3.
HCF = 3 × 3 = 9
Hence, the HCF of 18, 54, 81 is 9
(j) 12, 45, 75
The prime factorizations of 12, 45 and 75 are as follows:
12 = 2 × 2 × 3
45 = 3 × 3 × 5
75 = 3 × 5 × 5
The common factors, in this case, are 3.
HCF = 3
Hence, the HCF of 12, 45, 75 is 3
You can also use the HCF Calculator to answer this.
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 Question 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
Summary:
The HCF of the given numbers are a) 6, b) 6, c) 6, d) 9, e) 12, f) 34, g) 35, h) 7, i) 9, j) 3.
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