Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (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 $3^4=3^8=3^{12}=\dots .3^{100}$.
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 $2^4=2^8=2^{12}=\dots .2^{500}$.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.