**Playing with Numbers**

**Exercise 3.6**

**Ex 3.5 Question 1.**

**Find the HCF of the following numbers:**

**(a) 18, 48**

**(b) 30, 42**

**(c) 18, 60**

**(d) 27,63**

**(e) 36,84**

**(f) 34, 102**

**(g) 70, 105, 175**

**(h) 91, 112, 49**

**(i) 18, 54, 81**

**(j) 12, 45, 75**

**Solution:**

**(a) 18 and 48.**

Factors of 18 = 2 x 3 x 3

Factors of 48 = 2 x 2 x 2 x 2 x 2 x 3

Here, the common factors are 2 and 3.

Hence, the HCF = 2 x 3 = 6.

**(b) 30 and 42.**

Factors of 30 = 2 x 3 x 5

Factors of 42 = 2 x 3 x 7

Here, the common factors are 2 and 3.

Hence, the HCF = 2 x 3 = 6.

**(c) 18 and 60.**

Factors of 18 = 2 x 3 x 3

Factors of 60 = 2 x 2 x 3 x 5

Here, the common factors are 2 and 3.

Hence, the HCF of 18 and 60 = 2 x 3 = 6.

**(d) 27 and 63.**

Factors of 27 = 3 x 3 x 3

Factors of 63 = 3 x 3 x 7

Here, the common factor is 3 (occurring twice).

Hence, the HCF = 3 x 3 = 9.

**(e) 36 and 84.**

Factors of 36 = 2 x 2 x 3 x 3

Factors of 84 = 2 x 2 x 3 x 7

Here, the common factors are 2, 2, and 3.

Hence, the HCF = 2 x 2 x 3 = 12.

**(f) 34 and 102.**

Factors of 34 = 2 x 17

Factors of 102 = 2 x 3 x 17

Here, the common factors are 2 and 17.

Thus, HCF is 2 x 17 = 34.

**(g)70, 105, and 175.**

Factors of 70 = 2 x 5 x 7

Factors of 105 = 3 x 5 x 7

Factors of 175 = 5 x 5 x 7

Here, common factors are 5 and 7.

Hence, the HCF of 70, 105 and 175 is 5 x 7 = 35.

**(h)91, 112, and 49.**

Factors of 91 = 7 x 13

Factors of 112 = 2 x 2 x 2 x 2 x 7

Factors of 49 = 7 x 7

Here, the common factor is 7.

Hence, the HCF = 7.

**(i) 18, 54, and 81.**

Factors of 18 = 2 x 3 x 3

Factors of 54 = 2 x 3 x 3 x 3

Factors of 81 = 3 x 3 x 3 x 3

Here, the common factor is 3 (occurring twice).

Thus, the HCF = 3 x 3 = 9.

**(j) 12, 45, and 75.**

Factors of 12 = 2 x 2 x 3

Factors of 45 = 3 x 3 x 5

Factors of 75 = 3 x 5 x 5

Here, the common factor is 3.

Hence, the HCF = 3.

**Ex 3.6 Question 2.**

**What is the HCF of two consecutive**

**(a) numbers?**

**(b) even numbers?**

**(c) odd numbers?**

**Solution:**

(a) Common factor of two consecutive numbers is always 1.

Hence, the HCF = 1.

(b) Common factors of two consecutive even numbers are 1 and 2.

Hence, the HCF = 1 x 2 = 2.

(c) Common factor of two consecutive odd numbers is 1.

Hence, the HCF = 1.

**Ex 3.6 Question 3.**

**HCF of co-prime numbers 4 and 15 was found as follows by factorization:**

**4 = 2 x 2 and 15 = 3 x 15. Since there are no common prime factors, so HCF of 4 and 15 is 0.**

**Is the answer correct? If not, what is the correct HCF?**

**Solution:**

No, the answer is not correct.

The correct HCF of 4 and 15 is 1.