# NCERT Solutions for Class 6th Mathematics

## Chapter 3. Playing with Numbers

### Exercise 3.6

**Exercise -3.6**

**Q1. Find the H.C.F. of the following numbers:**

**(f) 34, 102 **

**Solutions: **

Prime factorization of 34

= 2 × 17

Prime factorization of 102

= 2 × 3 × 17

HCF of 34 and 102 is 2 × 17

= 34

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

**Solution:**

Prime factorization of 70

= 2 × 5 × 7

Prime factorization of 105

= 3 × 5 × 7

Prime factorization of 175

= 5 × 5 × 7

H.C.F. (70, 105, 175)

= 5 × 7

= 35

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

**Solution: **

Prime factorization of 91

= 7 × 13

Prime factorization of 112

= 2 × 2 × 2 × 2 × 7

Prime factorization of 49

= 7 × 7

H.C.F. (91, 112, 49) = 7

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

**Solution: **

Prime factorization of 18

= 2 × 3 × 3

Prime factorization of 54

= 2 × 3 × 3 × 3

Prime factorization of 81

= 3 × 3 × 3 × 3

H.C.F. = 3 × 3 = 9

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

**Solution: **

Prime factorization of 12

= 2 × 2 × 3

Prime factorization of 45

= 3 × 3 × 5

Prime factorization of 75

= 3 x 5 x 5

H.C.F. = 1 × 3

= 3

**Q2. What is the H.C.F. of two consecutive:**

**(a) numbers?**

**(b) even numbers?**

**(c) odd numbers? **

**Solution:**

(a) H.C.F. of two consecutive numbers be 1.

(b) H.C.F. of two consecutive even numbers be 2.

(c) H.C.F. of two consecutive odd numbers be 1.

**Q3. H.C.F. of co-prime numbers 4 and 15 was found as follows by factorization:**

**4 = 2 **×** 2 and **

**15 = 3 **×** 5 since there is no common prime factor, so H.C.F. of 4 and 15 is 0. Is the answer correct? If not, what is the correct H.C.F.? **

**Solution:** No. The correct H.C.F. is 1.