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

$$ 3^{1}=3,3^{2}=9,3^{3}=27,3^{4}=81,3^{5}=243 $$ Now, for power of 3 , the unit digit keep on repeating after power difference of 4 , So, unit digit for $3^{4}=3^{8}=3^{12}=\ldots .3^{100}$. 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 $2^{4}=2^{8}=2^{12}=\ldots .2^{500}$.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.