Page 45 - Maths Class 06

Exercise 3.3

1. Complete the following factor trees and write down the prime factors of each number:
(a) 90 (b) 84 (c) 180

2. Write the prime factorisation of each of the following number:
(a) 28 (b) 54 (c) 36 (d) 24
(e) 120 (f) 256 (g) 96 (h) 180
(i) 1024 (j) 2200 (k) 630 (l) 468

3. Find the prime factors of 1729.
4. Write the small est and the larg est 4-digit numbers and deter mine the prime factori sa tion of each.

Highest Common Factor (HCF)

As, the name suggests, the HCF is the greatest common factor of the given numbers, i e. . HCF is the highest
number that can divide given numbers completely.
e g. ., The HCF of 24 and 30 is 6 as
Factors of 24 = 1 , 2 , 3 , 4, 6 , 8, 12, 24

Factors of 30 = 1 , 2 , 3 , 5, 6 , 10, 15, 30
Clearly, the common factors are 1, 2, 3, and 6 are the greatest common factor is 6.
\ HCF of 24 and 30 is 6.

HCF is also known as greatest common divisor (GCD).
EX AM PLE 1. Find the HCF of 36 and 84.

SO LU TION : The prime factorisation of 36 and 84 are
2 36 2 84
36 = 2 2 3 3´ ´ ´
b b b 2 18 2 42

and 84 = 2 2 3 7´ ´ ´ 3 9 3 21
The common factors are 2, 2 and 3. 3 3 7 7

The product of these factors is 2 2 3´ ´ , i e. . 12.
1 1
Thus, 12 is the HCF of 36 and 84.

45