Class 10 Math Exercise 1.3 Solved – Euclid’s Lemma & HCF PDF

Class 10 Math Exercise 1.3 – Euclid’s Lemma & HCF Solved

📘 Introduction

Exercise 1.3 of Class 10 Mathematics focuses on the real number system using Euclid’s Division Lemma to find the HCF of two numbers. This solved guide helps weak students understand the logic, steps, and application of the lemma clearly.

🔍 What is Euclid’s Division Lemma?

Euclid's Lemma states: For any two positive integers a and b, there exist integers q and r such that:

a = bq + r, where 0 ≤ r < b

Using this, we apply repeated division to find the Highest Common Factor (HCF).

📝 Solved Questions in Exercise 1.3

• Q1: Use Euclid’s lemma to find HCF of given numbers
• Q2: Step-by-step division to reach remainder 0
• Q3: Proper explanation with logical statements

💡 Easy Method Steps:

1. Divide larger number by smaller number
2. Write in a = bq + r form
3. Repeat process with new values until remainder is 0
4. Last non-zero remainder is HCF

✅ Study Pool Certified

This solution guide is Study Pool Certified and Verified by M Usman (MSc Physics). All steps are explained clearly for board exam success.

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📥 Download Exercise 1.3 Solved PDF

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🔗 Related Exercises

🔁 Previous: Exercise 1.2 – Word Problems Solved

➡️ Next: Exercise 1.4 – Rational Numbers & Properties