Question

According to Euclid's division lemma, for given positive integers $a$ and $7$, there exit unique non negative integers $q$ and $r$ such that $a=7q+r$, where__________

• A. $0<r\le 7$
• B. $0\le r<7$
• C. $1\le r\le 7$
• D. $r\ge 7$

Answer 1

Answer: (B)

$0\le r<7$

According to the definition of Euclid's theorem,

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

so in this case ,

$a=7\times q+r$ where $0\le r<7.$