Question

If $n$ is a prime number greater than $3$, what is the remainder when $n^2$ is divided by $12$ ?

• A. $0$
• B. $1$
• C. $2$
• D. $3$
• E. $5$

Answer 1

The correct option is B $1$

n is the prime number greater then $3$.

so next prime number is $n=5$

so $5^2=25$ when it is divide by $12$ it gives remainder $1$.

take $n=7$

$7^2=49$ when it is divide by $12$ it gives remainder $1$.

take $n=11$

${11}^2=121$ when it is divide by $12$ it gives $1$ as remainder.

so from above we conclude that when a prime number which is greater then $3$ is divide by $12$ it always gives remainder as $1$.