EXERCISE 3.6

**1). Find the HCF of the following numbers:**

a) 18, 48

**Ans.** 18 = 2 x 3 x 3

48 = 2 x 2 x 2 x 2 x 3

∴HCF = 2 x 3 = 6

b) 30, 42

**Ans.** 30 = 2 x 3 x 5

42 = 2 x 3 x 7

∴HCF = 2 x 3 = 6

c) 18, 60

**Ans.** 18 = 2 x 3 x 3

60 = 2 x 2 x 3 x 5

∴HCF = 2 x 3 = 5

d) 27, 63

**Ans.** 27 = 3 x 3 x 3

63 = 3 x 3 x 7

∴HCF = 3 x 3 = 9

e) 36, 84

**Ans.** 36 = 2 x 2 x 3 x 3

84 = 2 x 2 x 3 x 7

∴HCF = 2 x 2 x 3 = 12

f) 34, 102

**Ans. **34 = 2 x 17

102 = 2 x 3 x 17

∴HCF = 2 x 17 = 34

g) 70, 105, 175

**Ans.**70 = 2 x 5 x 7

105 = 3 x 5 x 7

175 = 5 x 5 x 7

∴HCF = 5 x 7 = 35

h) 91, 112, 49

**Ans.**91 = 7 x 13

112 = 2 x 2 x 2 x 2 x 7

49 = 7 x 7

∴HCF = 7

i) 18, 54, 81

**Ans. **18 = 2 x 3 x 3

54 = 2 x 3 x 3 x 3

81 = 3 x 3 x 3 x 3

∴HCF = 3 x 3 = 9

j) 12, 45, 75

**Ans.** 12 = 2 x 2 x 3

45 = 3 x 3 x 5

75 = 3 x 5 x 5

∴HCF = 3

**2). What is the HCF of two consecutive Numbers?**

**Ans.** 1

**Eg:** The HCF of 2 and 3 is 1

Even numbers?

**Ans.**2

**Eg:** HCF of 2 and 4 is 2

Odd numbers?

**Ans.**1

**Eg:** HCF of 3 and 5 is 1

**3). HCF of co-prime numbers 4 and 15 was found as follows by factorisation:**

**4 = 2 x 2 and 15 = 3 x 5 since there is no common prime factors, so HCF of 4 and 15 is 0. Is the answer correct ? If not, what is the correct HCF**

**Ans**. No. The correct HCF is 1