Question

What will be the remainder if the number $7^{2015}$ is divided by $25$ ?

• A. $24$
• B. $18$
• C. $7$
• D. $1$

Answer 1

The correct option is B $18$

When divided by $25,$

$7^1$ gives remainder $7$

$7^2=49$ gives $24$

$7^3=343$ gives $18$

$7^4=2401$ gives $1$

$7^5=16807$ gives $7$

From the above we can see that,

The remainder repeat after every fourth power of $7.$

Now, $2015$ can be written as $=4\times 503+3$

$\Rightarrow$ $7^{2015}=7^{4\times 503+3}$ will leave a remainder $18$