What is the units digit of 2^99?

Question

(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

cska · Answer

e) 8 . 99:4, remainder 3

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kunalcvrce · Answer

unit digit of any number is always the remainder of 10 when that number is divided by 10.
Remainder
2/10=2 
2^2/10=4(by remainder theorem)
2^3/10=8(by remainder theorem)
2^4/10=6(by remainder theorem)
Now it will start repeating in grp of 4. So 99/4 remainder will be 3. so 
remainder will be same as 2^3/10=8

GMATBusters · Answer

Principle to calculate unit digit.
1) divide the exponent by 4, and find remainder.
2) unit digit of expression will be the unit digit of base raised to power of remainder.
If remainder is 0. Raise to power of 4.

Here the remainder 99/4 is 3
So answer will be unit digit of 2^3= 8

E

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AkshdeepS · Answer

2 has a cyclicity of 4 = 2 , 4 , 8 , 6

We have 99/4 = 24 rem 3

Therefore units digits of 2^99 will be the same as units digit of 2^3 = 8

(E)

shilpibansal · Answer

ans should be D
Unit digits of the powers of two
2^1=2
2^2=4
2^3=8
2^4=6
2^5=2...... and follows the same trend as above

So, 2^99=6 as unit digit

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

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

We need to find the units digit of  2^{99}

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 (99) by 4 and check what is the remainder
99 divided by 4 gives 3 remainder

=> Units digit of  2^{99}  = Units digit of  2^3  = 8

So,  Answer will be E 
Hope it helps!

Link to Theory for Last Two digits of exponents here    .

Link to Theory for Units' digit of exponents here    .

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What is the units digit of 2^99?

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What is the units digit of 2^99?

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