Exercise -3.6
Q1. Find the H.C.F. of the following numbers:
(f) 34, 102
Solutions:
Prime factorization of 34
= 2 × 17
Prime factorization of 102
= 2 × 3 × 17
HCF of 34 and 102 is 2 × 17
= 34
(g) 70, 105, 175
Solution:
Prime factorization of 70
= 2 × 5 × 7
Prime factorization of 105
= 3 × 5 × 7
Prime factorization of 175
= 5 × 5 × 7
H.C.F. (70, 105, 175)
= 5 × 7
= 35
(h) 91, 112, 49
Solution:
Prime factorization of 91
= 7 × 13
Prime factorization of 112
= 2 × 2 × 2 × 2 × 7
Prime factorization of 49
= 7 × 7
H.C.F. (91, 112, 49) = 7
(i) 18, 54, 81
Solution:
Prime factorization of 18
= 2 × 3 × 3
Prime factorization of 54
= 2 × 3 × 3 × 3
Prime factorization of 81
= 3 × 3 × 3 × 3
H.C.F. = 3 × 3 = 9
(j) 12, 45, 75
Solution:
Prime factorization of 12
= 2 × 2 × 3
Prime factorization of 45
= 3 × 3 × 5
Prime factorization of 75
= 3 x 5 x 5
H.C.F. = 1 × 3
= 3
Q2. What is the H.C.F. of two consecutive:
(a) numbers?
(b) even numbers?
(c) odd numbers?
Solution:
(a) H.C.F. of two consecutive numbers be 1.
(b) H.C.F. of two consecutive even numbers be 2.
(c) H.C.F. of two consecutive odd numbers be 1.
Q3. H.C.F. 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 factor, so H.C.F. of 4 and 15 is 0. Is the answer correct? If not, what is the correct H.C.F.?
Solution: No. The correct H.C.F. is 1.
