## What is Euclid Division lemma give example?

As per Euclid’s division lemma, for any two positive integers, say ‘a’ and ‘b’. the condition ‘a = bq +r’ , where 0 ≤ r < b. Mathematically we can represent it as ‘Dividend = (Divisor × Quotient) + Remainder. For example, 59 = (7 × 8) + 3.

**Does Euclid’s division lemma hold if a is a negative integer?**

Though Euclid division lemma has been stated for all positive integers only But it can be extended for negative integers too.. So that’s why Euclid’s division lemma is only applicable only for integers Except zero….

### Which option is correct for Euclid Division lemma?

Hence, option (c) is the correct option. Note: Euclid’s division lemma holds true unit a is prime. If a is a prime number, it can only be divided itself, so, b = a, q = 1 and r = 0.

**What do you mean by include division lemma?**

As per Euclid’s division lemma, for any two positive integers, say a and b, there exists unique integers q and r, such that a=bq+r; where 0≤rDividend=(Divisor×quotient)+Remainder.

## What is Euclid lemma method?

Euclid’s lemma — If a prime p divides the product ab of two integers a and b, then p must divide at least one of those integers a and b. It is used to define prime elements, a generalization of prime numbers to arbitrary commutative rings.

**Is BQ equal to r?**

Euclid’s division Lemma: Euclid’s division Lemma states that for any two positive integers ‘a’ and ‘b’ there exist two unique whole numbers ‘q’ and ‘r’ such that , a = bq + r, where 0≤ r < b. Here, a= Dividend, b= Divisor, q= quotient and r = Remainder. Hence, the values ‘r’ can take 0≤ r < b.

### What is the HCF of 960 and 432?

48

Answer: HCF of 960 and 432 is 48.

**What is Pythagorean triples formula?**

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a2 + b2 = c2; thus, Pythagorean triples describe the three integer side lengths of a right triangle.

## Who introduced division lemma?

Euclid’s Division Lemma

According to Euclid’s Division Lemma if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r < b. The basis of the Euclidean division algorithm is Euclid’s division lemma.

**What is the HCF of 81 and 675?**

Therefore, the HCF of 675 and 81 will be 27.