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### Impossible Word

```
Date: 04/14/2001 at 10:08:51
From: Dustin Babler
Subject: Word Values

What is a word that comes out to 575,151 when multiplying its letters'
values together?

For example, belch = 376,200 (25*22*15*24*19).

I have come close, but not close enough!

Dustin
```

```
Date: 04/16/2001 at 13:46:43
From: Doctor TWE
Subject: Re: Word Values

Hi Dustin - thanks for writing to Dr. Math.

The first thing I did when I saw this problem was to find the prime
factorization of 575151 because that would limit the possible letters
I had to work with. What I found out was that 575151 = 3*191717, and
191717 is a prime number. (I have a computer program that verified
that for me.)

Since there is no 191717th letter in our alphabet, the
construction must be impossible!

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Factoring Numbers
Middle School Puzzles

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