Class 10 Maths Chapter 1 Exercise 1.1 Solutions – Real Numbers | Assam Eduverse

Welcome to Assam Eduverse, your trusted source for Class 10 NCERT Maths solutions. Below is the complete solution of Class 10 Maths Chapter 1: Real Numbers (Exercise 1.1) as per the NCERT 2025–26 syllabus. The answers are provided with clear steps using the prime factorisation method, Euclid’s algorithm, and basic number theory.

📘 Chapter 1: Real Numbers

🧮 Exercise 1.1 – NCERT Solutions

✅ Question 1:

Express each number as a product of its prime factors:

(i) 140 = 2 × 2 × 5 × 7 = 2² × 5 × 7
(ii) 156 = 2 × 2 × 3 × 13 = 2² × 3 × 13
(iii) 3825 = 3 × 3 × 5 × 5 × 17 = 3² × 5² × 17
(iv) 5005 = 5 × 7 × 11 × 13 = 5 × 7 × 11 × 13
(v) 7429 = 17 × 19 × 23 = 17 × 19 × 23

✅ Question 2:

Find the LCM and HCF of the following pairs and verify LCM × HCF = Product of numbers.

(i) 26 and 91

• 26 = 2 × 13

• 91 = 7 × 13
  ➡️ HCF = 13, LCM = 2 × 7 × 13 = 182
  ✔ 26 × 91 = 2366, and 13 × 182 = 2366 ✅

(ii) 510 and 92

• 510 = 2 × 3 × 5 × 17

• 92 = 2 × 2 × 23
  ➡️ HCF = 2, LCM = 2² × 3 × 5 × 17 × 23 = 23460
  ✔ 510 × 92 = 46920, and 2 × 23460 = 46920 ✅

(iii) 336 and 54

• 336 = 2⁴ × 3 × 7

• 54 = 2 × 3³
  ➡️ HCF = 2 × 3 = 6, LCM = 2⁴ × 3³ × 7 = 3024
  ✔ 336 × 54 = 18144, and 6 × 3024 = 18144 ✅

✅ Question 3:

Find the LCM and HCF by using prime factorisation method.

(i) 12, 15 and 21

• 12 = 2² × 3

• 15 = 3 × 5

• 21 = 3 × 7
  ➡️ HCF = 3, LCM = 2² × 3 × 5 × 7 = 420

(ii) 17, 23 and 29
All are prime numbers.
➡️ HCF = 1, LCM = 17 × 23 × 29 = 11339

(iii) 8, 9 and 25

• 8 = 2³

• 9 = 3²

• 25 = 5²
  ➡️ HCF = 1, LCM = 2³ × 3² × 5² = 1800

✅ Question 4:

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

Using the identity:
LCM × HCF = Product of the numbers
⇒ LCM = (306 × 657) ÷ 9 = 22338

✅ Question 5:

Check whether 6ⁿ can end with the digit 0 for any natural number n.

6ⁿ = (2 × 3)ⁿ contains only factors of 2 and 3.
To end in 0, a number must be divisible by 5.
➡️ Since there’s no factor of 5, 6ⁿ can never end with 0 ✅

✅ Question 6:

Explain why the following are composite numbers:

(i) 7 × 11 × 13 + 13 = 1001 + 13 = 1014 = 13 × 78
✅ Composite number.

(ii) 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 = 5040 + 5 = 5045 = 5 × 1009
✅ Composite number.

✅ Question 7:

A circular path: Sonia takes 18 min, Ravi takes 12 min. Find after how many minutes they meet again.

Find LCM(18, 12)

• 18 = 2 × 3²

• 12 = 2² × 3
  ➡️ LCM = 2² × 3² = 36 minutes
  ✅ They will meet again after 36 minutes.