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The remainder when `5^2004`  is divided by 100 is A)75 B)50 C)25 D)5 E)10

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christiano-cr7 | Salutatorian

Posted July 1, 2013 at 3:44 PM via web

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The remainder when `5^2004`  is divided by 100 is

A)75

B)50

C)25

D)5

E)10

1 Answer | Add Yours

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ishpiro | Teacher | (Level 1) Associate Educator

Posted July 1, 2013 at 3:51 PM (Answer #1)

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Let's consider a few powers of 5:

`5^1 = 5`

`5^2 = 25`

`5^3 = 125`

`5^4 = 625`

`5^5 = 3125` 

It is apparent that every power of 5 higher than 2 can be expressed as

100n + 25, where n is an integer

So the remainder of `5^2004` divided by 100 is 25.

The answer is C, 25.

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