Find the remainder of 2^100/12

Find the remainder of 2^100/12

A. 4
B. 2
C. 8
D. 1
E. none

The OA is the option A.

Is there a simple way to solve this PS question? I can I solve it? I'd appreciate your help.

Hi Vincen,
Let's take a look at your question.

We need to find the remainder of
$$\frac{2^{100}}{12}$$
$$=\frac{2^{2\times50}}{12}$$
$$=\frac{4^{50}}{12}$$

Let's check what happens when powers of 4 is divided by 12, starting from 4^2.
$$4^2=16$$
$$\frac{16}{12}=1\ remainder\ 4$$

$$4^3=64$$
$$\frac{64}{12}=5\ remainder\ 4$$

$$4^4=256$$
$$\frac{256}{12}=21\ remainder\ 4$$

$$4^5=1024$$
$$\frac{1024}{12}=85\ remainder\ 4$$

Which shows that remainder is 4 for all the positive powers of 4.
Therefore, option A is correct.

Hope it helps.
I am available if you'd like any follow up.