Question

What is the unit place digit of 2^2250

Answer 1

Let's consider the lowest power of 2.

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

2^5 = 32

2^6 = 64

2^8 = 128

2^9 = 256

2^10 = 512

Now since we are concerned only about the digit at the unit's place, we can see here that the pattern 2, 4, 8, 6 is repeating after every 4th cycle.

Let's get back to the question.

We have 2^2250. Now 2250 can be written as-

2250=2248+2

Further
2^2250=2^2248+2^2

from the observation made above that the sequence repeats itself after 4th cycle....

So
2^2249.........(2 at unit place)

2^2250........(4 at unit place)

Hence the answer is 4.

Hope it helps...... :)