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NCERT Solutions for Class 10 Maths Chapter 1 : Real Number

Real Number
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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

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

 

 

NCERT 10th Maths Ch 1 EX 1.1 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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

 

 

NCERT 10th Maths Ch 1 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.

 

 

NCERT Solutions for Class 10 Maths Chapter 1 Real Number – Ex 1.3

 

 

NCERT 10th Maths Ch 1 EX 1.3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

NCERT Solutions for Class 10 Maths Chapter 1 Real Number – Ex 1.4

 

 

NCERT 10th Maths Ch 1 EX 1.4

 

 

 

 

 

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