Question

According to Euclid's division lemma, if $a$ and $b$ are two positive integers with $a>b,$ then which of the following is true? (Here, $q$ and $r$ are unique integers.)

• A. $a=b\times r$ where $0\le r<b$
• B. $b=aq+r$ where $0\le r<a$
• C. $a=b+r$ where $0\le r<a$
• D. $a=bq+r$ where $0\le r<b$

Answer 1

The correct option is D

$a=bq+r$ where $0\le r<b$

Euclid's division lemma states that for positive integers $a$ and $b,$ where $(a>b),$ there exist unique integers $q$ and $r$ such that $a=b\times q+r,$ where $0\le r<b.$