Q. Find the highest common factor (HCF) by prime factorisation. One has been done for you:- (a) 44,28 44 = 2 x 2 x 11 28= 2x2x7 HCF = 2 x 2 = 4 (c) 22, 44 22= 44 = HCF = (e) 63,36 63= 36= HCF = 8 (b) 45,75 45 = 75 = HCF = (d) 75,25 75 = 25 = HCF = (f) 86,64 86= 64= HCF =
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Verified answer
(a) HCF of 44 and 28 = 4
(b) HCF of 45 and 75 = 15
(c) HCF of 22 and 44 = 22
(d) HCF of 75 and 25 = 25
(e) HCF of 63 and 36 = 9
(f) HCF of 86 and 64 = 2
Given:
Some numbers are given.
To Find:
The HCF of the given numbers by prime factorization.
Solution:
(a) 44 and 28:
The prime factorization is
44 = 2² × 11
28 = 2² × 7
HCF of 44 and 28 = Common factors of 44 and 28
HCF of 44 and 28 = 2²
HCF of 44 and 28 = 4
(b) 45 and 75:
The prime factorization is
45 = 3² × 5
75 = 3 × 5²
HCF of 45 and 75 = Common factors of 45 and 75
HCF of 45 and 75 = 3 × 5
HCF of 45 and 75 = 15
(c) 22 and 44:
The prime factorization is
22 = 2 × 11
44 = 2² × 11
HCF of 22 and 44 = Common factors of 22 and 44
HCF of 22 and 44 = 2 × 11
HCF of 22 and 44 = 22
(d) 75 and 25:
The prime factorization is
75 = 3 × 5²
25 = 5²
HCF of 75 and 25 = Common factors of 75 and 25
HCF of 75 and 25 = 5²
HCF of 75 and 25 = 25
(e) 63 and 36:
The prime factorization is
63 = 3² × 7
36 = 2² × 3²
HCF of 63 and 36 = Common factors of 63 and 36
HCF of 63 and 36 = 3²
HCF of 63 and 36 = 9
(f) 86 and 64:
The prime factorization is
86 = 2 x 43
64 = 2⁶
HCF of 86 and 64 = Common factors of 86 and 64
HCF of 86 and 64 = 2
(a) HCF of 44 and 28 = 4
(b) HCF of 45 and 75 = 15
(c) HCF of 22 and 44 = 22
(d) HCF of 75 and 25 = 25
(e) HCF of 63 and 36 = 9
(f) HCF of 86 and 64 = 2
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