What is the units digit of 2^39?

Question

A) 2
(B) 4
(C) 6
(D) 8
(E) 9

NandishSS · Answer

2^39 ==> Cyclic order of 2 is 4

2^1=2
2^2=4
2^3=8
2^4=6
2^5=2
.
.
.
.
Here unit digit of 2^39==> 2^3==>8

Hence D

TheNightKing · Answer

Units digit of 2 (Cycle) 2 2*2=4 4*2=8 8*2=6 6*2=2 Repeat. So we have a cycle of 4. To find unit digit of 2^39, we need to realise 36 out of 39 will be 9 cycles. The remainder is 3. And at third position of cycle we have 8. So answer is Option D (8) P.S: This is posted on Feb 29,2020. Let's see if I am around to come back to check this Post on Feb 29,2024.

CrackverbalGMAT · Answer

The cyclicity of the digits are as given below

0,1,5 and 6 have a cyclicity of 1

4 and 9 (the perfect squares) have a cyclicity of 2

All others i.e 2, 3, 7 and 8 have a cyclicity of 4.

To Find the units place of  a^b  , where a is the base and b is the power.

Divide the power by the cyclicity of the base and find the remainder.

Here 2 cases arise.

Case 1:     If the remainder = 0

For base ending in 2, 4 or 8 the last digit will be 6

For base ending in 3, 7 or 9 the last digit will be 1

Case 2:     If the remainder  
eq 0 , then the last digit will be the base to the power of the remainder.

In the question given above: To find the units place of  2^{39}

The base is 2 whose cyclicity is 4 and the power is 39

R    = 3

The base raised to the power gives the answer =  2^3  = 8

Option D

Arun Kumar

BrushMyQuant · Answer

We need to find the units digit of  2^{39}

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 2 has a cycle of 4

=> We need to divide the power (39) by 4 and check what is the remainder
39 divided by 4 gives 3 remainder

=> Units digit of  2^{39}  = Units digit of  2^3  = 8

So,  Answer will be D 
Hope it helps!

Link to Theory for Last Two digits of exponents here    .

Link to Theory for Units' digit of exponents here    .

What is the units digit of 2^39?

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What is the units digit of 2^39?

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