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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.

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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.

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