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.
NCERT Solutions for Class 10 Maths Chapter 1 Real Number – Ex 1.3
NCERT Solutions for Class 10 Maths Chapter 1 Real Number – Ex 1.4
