Question

If $a=107,b=13$ using Euclid's division algorithm find the values of $q$ and $r$ such that $a=bq+r$

• A. $q=8,r=8$
• B. $q=8,r=3$
• C. $q=0,r=3$
• D. None of these

Answer 1

The correct option is B $q=8,r=3$

According to the definition of Euclid's theorem,

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

$\frac{a}{b}=\frac{107}{13}=\frac{104+3}{13}=8+\frac{3}{13}$

$⟹$ quotient $=8,$ remainder $=3$

Using Euclid's algorithm $q=8,r=3$