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 (a)
18, 48
Let’s find the prime factors of 18 and 48.
2 and 3 are common prime factors.
Therefore, H.C.F
Solution (b)
30, 42
Let’s find the prime factors of 30 and 42.
2 and 3 are common prime factors of 30 and 42.
Therefore, H.C.F
Solution (c)
18, 60
Let’s find the prime factors of 18 and 60.
2 and 3 are the common prime factors.
Therefore, H.C.F
Solution (d)
27, 63
Let’s find the prime factors of 27 and 63.
3 and 3 are the common prime factors.
Therefore, H.C.F
Solution (e)
36, 84
Let’s find the prime factors of 36 and 84.
2, 2 and 3 are the common prime factors.
Therefore, H.C.F
Solution (f)
34, 102
Let’s find the prime factors of 34 and 102.
2 and 17 are the common prime factors.
Therefore, H.C.F
Solution (g)
70, 105, 175
Let’s find the prime factors of 70, 105 and 175.
5 and 7 are the common prime factors.
Therefore, H.C.F
Solution (h)
91, 112, 49
Let’s find the prime factors of 91, 112 and 49.
7 is the only common prime factor.
Therefore, H.C.F = 7
Solution (i)
18, 54, 81
Let’s find the prime factors of 18, 54 and 81.
3 and 3 are the common prime factors.
Therefore, H.C.F
Solution (j)
12, 45, 75
Let’s find the prime factors of 12, 45 and 75.
3 is the only common prime factor.
Therefore, H.C.F = 3
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