Open App

Class 10 Exam > Class 10 Videos > 02 - HCF & Euclid's Division Lemma - Class 10 - Maths

02 - HCF & Euclid's Division Lemma - Class 10 - Maths Video Lecture

Q: 3. How is Euclid's Division Lemma used to find the HCF of two numbers?

Ans. Euclid's Division Lemma is used to find the HCF of two numbers by repeatedly applying the division algorithm. We divide the larger number by the smaller number and obtain the remainder 'r'. Then we replace the larger number with the smaller number and the smaller number with the remainder obtained. We repeat this process until the remainder becomes zero. The divisor at this point will be the HCF of the two numbers.

Q: 4. Can the HCF of two numbers be greater than the smaller number?

Ans. No, the HCF of two numbers cannot be greater than the smaller number. The HCF is always a common factor of both numbers, and it must be smaller or equal to the smaller number. For example, the HCF of 12 and 18 cannot be greater than 12.

Q: 5. Is the HCF of two numbers always a prime number?

Ans. No, the HCF of two numbers is not always a prime number. The HCF can be any common factor of the given numbers, which may or may not be a prime number. For example, the HCF of 12 and 16 is 4, which is not a prime number.

FAQs on 02 - HCF & Euclid's Division Lemma - Class 10 - Maths Video Lecture

1. What is HCF and how is it calculated?

Ans. HCF stands for Highest Common Factor, which is the largest number that divides two or more given numbers without leaving any remainder. To calculate the HCF, we can use the prime factorization method or the division method.

2. What is Euclid's Division Lemma?

Ans. Euclid's Division Lemma states that for any two positive integers 'a' and 'b', there exist unique integers 'q' and 'r' such that a = bq + r, where 0 ≤ r < b. This lemma helps in finding the HCF of two numbers.

3. How is Euclid's Division Lemma used to find the HCF of two numbers?

Ans. Euclid's Division Lemma is used to find the HCF of two numbers by repeatedly applying the division algorithm. We divide the larger number by the smaller number and obtain the remainder 'r'. Then we replace the larger number with the smaller number and the smaller number with the remainder obtained. We repeat this process until the remainder becomes zero. The divisor at this point will be the HCF of the two numbers.

4. Can the HCF of two numbers be greater than the smaller number?

Ans. No, the HCF of two numbers cannot be greater than the smaller number. The HCF is always a common factor of both numbers, and it must be smaller or equal to the smaller number. For example, the HCF of 12 and 18 cannot be greater than 12.

5. Is the HCF of two numbers always a prime number?

Ans. No, the HCF of two numbers is not always a prime number. The HCF can be any common factor of the given numbers, which may or may not be a prime number. For example, the HCF of 12 and 16 is 4, which is not a prime number.

About this Video

3.2K Views

4.91/5 Rating

Oct 04, 2025 Last updated

Related Exams

Class 10

02 - HCF & Euclid's Division Lemma - Class 10 - Maths for Class 102025 is part of Class 10 preparation. The notes and questions for 02 - HCF & Euclid's Division Lemma - Class 10 - Maths have been prepared according to the Class 10 exam syllabus. Information about 02 - HCF & Euclid's Division Lemma - Class 10 - Maths covers all important topics for Class 102025 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for 02 - HCF & Euclid's Division Lemma - Class 10 - Maths.

Introduction of 02 - HCF & Euclid's Division Lemma - Class 10 - Maths in English is available as part of our Class 10 preparation & 02 - HCF & Euclid's Division Lemma - Class 10 - Maths in Hindi for Class 10 courses. Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.

Description

Video Lecture & Questions for 02 - HCF & Euclid's Division Lemma - Class 10 - Maths Video Lecture - Class 10 full syllabus preparation | Free video for Class 10 exam.

Information about 02 - HCF & Euclid's Division Lemma - Class 10 - Maths

Here you can find the 02 - HCF & Euclid's Division Lemma - Class 10 - Maths defined & explained in the simplest way possible. Besides explaining types of 02 - HCF & Euclid's Division Lemma - Class 10 - Maths theory, EduRev gives you an ample number of questions to practice 02 - HCF & Euclid's Division Lemma - Class 10 - Maths tests, examples and also practice Class 10 tests.

Summary

practice quizzes

Exam