Question

1. Find the HCF of the following numbers.

a) 13 and 169
b) 16 and 144
c) 18 and 72
d) 20 and 60
e) 25 and 225
f) 15 and 105​

Answer 1

Answer:

a)hcf of 13 and 169 =13

b)16

c)18

Answer 2

a) 13 and 169

13 = 1 x 13

169 = 13 x 13

HCF (13, 169) = 13

___________________

b) 16 and 144

16 = 2 x 2 x 2 x 2

144 = 3 x 3 x 2 x 2 x 2 x 2

HCF (16, 144) = 2 x 2 x 2 x 2 = 16

____________________

c) 18 and 72

18 = 2 x 3 x 3

72 = 3 x 3 x 2 x 2 x 2

HCF (18, 72) = 2 x 3 x 3 = 18

_____________________

d) 20 and 60

20 = 2 x 2 x 5

60 = 2 x 2 x 3 x 5

HCF (20, 60) = 2 x 2 x 5 = 20

_____________________

e) 25 and 225

25 = 5 x 5

225 = 3 x 3 x 5 x 5

HCF (25, 225) = 5 x 5 = 25

_____________________

f) 15 and 105​

15 = 3 x 5

105 = 3 x 5 x 7

HCF (15, 105) = 3 x 5 = 15

Highest Common Factor (or) Greatest Common Factor [HCF/GCF]

HCF (or GCF) refers the the product of the common factors present in the prime factorization of two given numbers. It is the highest number by which both the numbers can be divided without leaving a remainder.

Lowest Common Multiple [LCM]

The lowest common multiple is the least common multiple of two given numbers obtained by multiplying the greatest time each of the prime factors occur in the factorization process.

Relation between LCM, HCF and the numbers

Product (LCM, HCF) = Product (Numbers)

That is, HCF (a, b) x LCM (a, b) = a x b