What is the units digit of 2^2222?

Question

What is the units digit of  2^{2222} ?

A. 0
B. 2
C. 4
D. 6
E. 8

GMATCoachBen · Answer

First, find the units digit pattern for powers of 2:

2^1 = 2 (1st step in our pattern)
2^2 = 4 (2nd step)
2^3 = 8 (3rd step)
2^4 = 16 (4th step)

Note that if we continue writing out the pattern, we only need to multiply the units digit of 16 by 2 (we only care about the "6", not the "1")

2^5 --> 6*2 = 12 --> ends in 2

We can see that the pattern repeats for every 4 numbers: 2, 4, 8, 6...

Therefore, if the power is a multiple of 4, the units digit will be a 6.

For example: 
2^40 ends in a 6
2^41 ends in a 2
2^42 ends in a 4
2^43 ends in an 8
2^44 ends in a 6

So, the next step is to find where the power of 2222 lands in the pattern.

The quickest way is to notice that 2220 is a multiple of 4, because the last 2 digits are a multiple of 4. Therefore, 2^2220 would end in a 6.

So, 2222 is 2 steps farther in our pattern, which goes "2,4,8,6", and therefore ends in a  4, so the answer is C.

To become very quick and accurate on these, flashcards are helpful, such as the ones below:

BrushMyQuant · Answer

↧↧↧ Detailed Video Explanation to the Problem ↧↧↧

https://www.youtube.com/watch?v=iByFR6KPBdc

We need to find the units digit of  2^{2222}

Lets start by finding the cyclicity of units' digit in powers of 2

2^1  units’ digit is 2
 2^2  units’ digit is 4
 2^3  units’ digit is 8
 2^4  units’ digit is 6
 2^5  units’ digit is 2

That means that units digit of power of have a cycle of 4

=> We need to divide the power (2222) by 4 and check what is the remainder
2222 divided by 4 gives 2 remainder

=> Units digit of  2^{2222}  = Units digit of  2^2  = 4

So,  Answer will be C 
Hope it helps!

MASTER how to find Units digit of Power of 2

https://www.youtube.com/watch?v=SRwrXbOPquA

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

What is the units digit of 2^2222?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

What is the units digit of 2^2222?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards