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What is the remainder when 2^20 is divided by 10

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by mbawisdom » Tue Mar 06, 2018 3:30 pm
lheiannie07 wrote:What is the remainder when 2^20 is divided by 10 ?

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

Can some experts show me how to solve this problem?

OA D
The remainder when divided by 10 is the same as asking what is the units digit.
I know 2^10 = 1024 (you should memorise every power of 2 up to 10 --> it will speed you up!)
so 2^20 is (1024)*(1024) - the units digit of this multiplication is 6 (multiply 4*4 and take the units digit). Hence, the remainder is 6.

Answer is D.
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by [email protected] » Tue Mar 06, 2018 5:03 pm
Hi lheiannie07,

We're asked for the remainder when 2^20 is divided by 10.

To start, the GMAT would never expect you to calculate a number as big as 2^20, so there must be a pattern behind 'powers of 2' (and there is). The units digit of the powers of 2 follows a consistent pattern:

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16

2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256

Notice that the units digits follow the pattern: 2, 4, 8, 6.... 2, 4, 8, 6

The 20th power would be 5 groups of 4 values - and it would be the 4th value of that last group. Thus, it will equal 6.

Final Answer: D

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