Question

When 22015 is completely calculated, the units place of the number obtained is

pls answer if you know :)

Answer 1

☆ ANSWER ☆:-

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 2^2015. Now 2015 can be written as-

2015 = 2012 + 3

Further

2^2015 = (2^2012).(2^3)

Now 2^2012 will have 6 at the unit's place (from the observation made above that the sequence repeats itself after 4th cycle).

After 2012, the sequence 2, 4, 8, 6 will repeat.

2^2013 = …..2 (unit's place)

2^2014 = …..4 (unit's place)

2^2015 = …..8 (unit's place)

Hence the answer is 8.

Note:- In these type of questions, no matter how high the power is, just try to find the sequence that exist. Rest will work automatically.

Thank you!