Question

A number divided by $6$ leaves a remainder $3$. When the square of the number is divided by $6$, the remainder is:

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is D $3$

We know,

Remainder formula: Dividend = Quotient x Divisor + Remainder.

Let $x=6q+3$
Then, $x^2={(6q+3)}^2$
$=36q^2+36q+9$
$=6(6q^2+6q+1)+3$

Thus, when $x^2$ is divided by $6$, then remainder $=3$.