**NCERT Solutions** for Class 10 Maths Chapter 1: Real Number by Swiflearn are by far the best and most reliable NCERT Solutions that you can find on the internet. These NCERT Solutions for Class 10 Maths Chapter 1 are designed as per the CBSE Class 10th Maths Syllabus. These NCERT Solutions will surely make your learning convenient & fun. Students can also Download FREE PDF of NCERT Solutions Class 10 Chapter 1.

NCERT Maths Class 10 Chapter 1 is Real Numbers and has four exercises in it. **Swiflearn’s** solutions for all exercises are as per given in the NCERT Maths Class 10.

### NCERT Solutions for Class 10 Maths Chapter 1 Real Number – Ex 1.1

### NCERT Solutions for Class 10 Maths Chapter 1 Real Number – Ex 1.2

**Question 1:**

**Express each number as a product of its prime factors:**

**(i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429**

**Solution**:

(i) LCM of 140 = 2 × 2 × 5 × 7 = 22 × 5 × 7

(ii) LCM of 156 = 2 × 2 × 3 × 13 = 22 × 3 × 13

(iii) LCM of 3825 = 3 × 3 × 5 × 5 × 17 = 32 × 52 × 17

(iv) LCM of 5005 = 5 × 7 × 11 × 13

(v) LCM of 7429 = 17 × 19 × 23

**Question 2:**

**Find the LCM and HCF of the following pairs of integers and verify that**

**LCM × HCF = product of the two numbers.**

**(i) 26 and 91**

**(ii) 510 and 92**

**(iii) 336 and 54**

**Solution**:

(i) 26 and 91

26 = 2 × 13

91 = 7 × 13

As we know that 13 is the “largest number” which divides both 26 and 91. So, HCF will be = 13.

LCM = 2 × 7 × 13 = 182

Product of the two number will = 26 × 91 = 2366

HCF × LCM = 13 × 182

= 2366

As a result, product of two numbers = HCF × LCM

(ii) 510 and 92

510 = 2 × 3 × 5 × 17

92 = 2 × 2 × 23

2 is the “largest number” which divides both 510 and 92. So, HCF = 2.

LCM = 2 × 2 × 3 × 5 × 17 × 23

= 23460

Product of the two numbers = 510 × 92

= 46920

HCF × LCM = 2 × 23460 = 46920

As a result, product of two numbers = HCF × LCM

(iii) 336 and 54

336 = 2 × 2 × 2 × 2 × 3 × 7 = 24 × 3 × 7

54 = 2 × 3 × 3 × 3 = 2 × 33

6 is the “largest number” which divides both 336 and 54. So, HCF = 6.

LCM = 24 × 33 × 7

= 3024

Product of the numbers = 336 × 54

= 18144

HCF × LCM = 6 × 3024 = 18144

As a result, product of two numbers = HCF × LCM

**Question 3:**

**Find the LCM and HCF of the following integers by applying the prime**

**factorization method.**

**(i) 12, 15 & 21**

**(ii) 17, 23 & 29**

**(iii) 8, 9 & 25**

**Solution**:

(i) 12, 15 & 21

12 = 22 × 3

15 = 3 × 5

21 = 3 × 7

3 is the “largest number” which divides 12, 15 and 21. So, HCF = 3.

LCM = 22 × 3 × 5 × 7 = 420

(ii) 17, 23 & 29

17 = 1 × 17

23 = 1 × 23

29 = 1 × 29

1 is the largest number which divides 17, 23 and 29. So, HCF = 1.

LCM = 17 × 23 × 29 = 11339

(iii) 8, 9 & 25

8 = 2 × 2 × 2

9 = 3 × 3

25 = 5 × 5

1 is the largest number which divides 8, 9 and 25. So, HCF = 1.

LCM = 2 × 2 × 2 × 3 × 3 × 5 × 5 = 1800

**Question 4:**

**Given that HCF (306, 657) = 9, find LCM (306, 657).**

**Solution 4:**

HCF (306, 657) = 9

We know that, Product of two numbers is equal to product of their LCM and HCF.

**Question 6:**

**Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite**

**numbers.**

**Solution**:

As we know that there are two types of numbers, namely – prime and composite. Prime numbers have only two factors namely 1 and the number itself whereas composite numbers have factors other than 1 and itself.

So it can be observed that

7 × 11 × 13 + 13 = 13 × (7 × 11 + 1) = 13 × (77 + 1)

= 13 × 78

= 13 × 13 × 6

The given expression has 6 and 13 as its factors. As a result, it is a composite number.

7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 = 5 × (7 × 6 × 4 × 3 × 2 × 1 + 1)

= 5 × (1008 + 1)

= 5 × 1009

1009 cannot be factorized further. As a result, the given expression has 5 and 1009 as its factors. As a result, it is a composite number.