Question

The remainder when $3^{100}\times 2^{500}$ is divided by $5$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

$3^1=3,3^2=9,3^3=27,3^4=81,3^5=243$

Now, for power of $3$, the unit digit keep on repeating after power difference of $4$, So, unit digit for $3^4=3^8=3^{12}=....3^{100}$.So unit digit is $1$

$2^1=2,2^2=4,2^3=8,2^4=16,2^5=32$

Now, for power of $2$, the unit digit keep on repeating after power difference of $5$, So, unit digit for $2^4=2^8=2^{12}=....2^{500}$.So, unit digit is $6$.

So, the last digit of the product will be $6$. Dividing by $5$ we will have $1$ as a remainder.