Question

............. states that for any two positive integers $a$ and $b$ we can find two whole numbers $q$ and $r$ such that $a=b\times q+r$ where $0\le r<b.$

• A. Euclid's addition lemma
• B. Euclid's subtraction lemma
• C. Euclid's multiplication lemma
• D. Euclid's division lemma

Answer 1

Answer: (D)

Euclid's division lemma

Let the two positive integers be $a$, a dividend and $b$, a divisor.

We can find two whole numbers, $q$ and $r$ such that $q$ is the quotient and $r$ is the remainder.

So, $a=b\times q+r$ where $0\le r<b.$

This is Euclid's Division Lemma.

Hence, option D is correct.