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Euclid's Division Lemma Video Lecture - Class 10
FAQs on Euclid's Division Lemma Video Lecture - Class 10
| 1. What is Euclid's Division Lemma? |  |
Ans. Euclid's Division Lemma states that for any positive integers a and b, there exist unique integers q and r, such that a = bq + r, where 0 ≤ r < b.
| 2. How is Euclid's Division Lemma useful in solving problems related to divisibility? | |
Ans. Euclid's Division Lemma provides a way to express any positive integer a as a multiple of another positive integer b, plus a remainder. This helps in determining if a number is divisible by another number and finding factors or divisors of a given number.
| 3. Can you provide an example to illustrate Euclid's Division Lemma? | |
Ans. Sure! Let's consider a = 17 and b = 5. According to Euclid's Division Lemma, we can write 17 = 5 * 3 + 2, where 3 is the quotient (q) and 2 is the remainder (r).
| 4. How can Euclid's Division Lemma be used to find the HCF (Highest Common Factor) of two numbers? | |
Ans. Euclid's Division Lemma can be used to find the HCF of two numbers by repeatedly applying the lemma. Starting with the two given numbers, we divide the larger number by the smaller number using the lemma. We continue this process with the divisor and the remainder until the remainder becomes zero. The divisor at this stage will be the HCF of the two numbers.
| 5. Are there any limitations to Euclid's Division Lemma? | |
Ans. Yes, Euclid's Division Lemma has certain limitations. It is applicable only for positive integers and cannot be extended to negative numbers or fractions. Additionally, it assumes that the divisor (b) is always positive.
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Nov 16, 2024 Last updated |
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