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### 21^100 - Last Two Digits

```
Date: 09/04/97 at 21:19:52
From: K
Subject: 21^100

What are the last two digits of 21 to the 100th power?
```

```
Date: 09/05/97 at 07:32:48
From: Doctor Anthony
Subject: Re: 21^100

The last two digits follow a pattern:

Number        Last two digits
21               21
21^2             41
21^3             61
21^4             81
21^5             01
21^6             21
21^7             41

and so on.

The last digit is always 1, and the second to last goes through the
sequence

2, 4, 6, 8, 0,    2, 4, 6, 8, 0,

So every 5th power gives the same final two digits.

Powers of 5, 10, 15, ......, 90, 95, 100  will all have 01 as the
final two digits.

The last two digits of 21^100  are  01

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Exponents
High School Sequences, Series
Middle School Exponents

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