Page 46 - Maths Class 06

EX AM PLE 2. Find the HCF of 16, 48 and 80.
SO LU TION : The prime factorisation of 16, 48 and 80 are
16 = 2 2 2 2´ ´ ´ 2 16 2 48 2 80
b b b b
2 8 2 24 2 40
48 = 2 2 2 2 3´ ´ ´ ´
2 4 2 12 2 20
b b b b
2 2 2 6 2 10
80 = 2 2 2 2 5´ ´ ´ ´
1 3 3 5 5
The common factors are 2, 2, 2 and 2.
The product of these factors is 2 2 2 2´ ´ ´ , i e. . 16. 1 1

Thus, 16 is the HCF of 16, 48 and 80.
EX AM PLE 3. Find the HCF of 70, 105 and 225.

SO LU TION : The prime factorization of 70, 105 and 225 are
70 = 2 5 7´ ´ 2 70 3 105 3 225
b
5 35 5 35 3 75
105 = 3 5 7´ ´
7 7 7 7 5 25

1 1 5 5
225 = 3 3 5 5´ ´ ´
The common factors are 5. 1
Thus, 5 is the HCF of 70, 105 and 225.

NOTE

Of the two numbers, if one number is a factor of the other, the smaller number is the HCF of the given numbers.
If two numbers are co-primes, their HCF is 1.
The HCF of two consecutive:
(a) numbers is 1; (b) even number is 2; (c) odd numbers is 1.

Exercise 3.4

1. Find the HCF of:
(a) 35, 45 (b) 30, 42 (c) 18, 48 (d) 18, 60

(e) 38, 25 (f) 60, 72 (g) 27, 63 (h) 36, 84
(i) 42, 72 (j) 34, 102 (k) 81, 405 (l) 90, 108
2. Find the HCF of:
(a) 12, 45 and 75 (b) 16, 48 and 60 (c) 15, 30 and 75

(d) 49, 91, 112 (e) 36, 126 and 180 (f) 18, 54 and 81

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