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### Prime Factor Puzzle

```Date: 10/24/2003 at 10:43:56
From: Stephen
Subject: prime factors

The two prime factors of a number are greater than 12 but less than
25.  The number is greater than 300 but less than 400.  What is the
number?  What are the factors?
```

```
Date: 10/25/2003 at 19:49:33
From: Doctor Ian
Subject: Re: prime factors

Hi Stephen,

Let's look at a smaller version of the problem.

The two prime factors of a number are greater than 3 but
less than 10.  The number is greater than 30, but less
than 40.  What are the factors?

First, we have to find all the prime numbers between 3 and 10.  The
first several prime numbers are

2, 3, 5, 7, 11, 13, ...

so the ones we're interested in are 5 and 7.  Now, how many numbers c
can be make with those prime factors?

x     5   7
--------
|
5 |  25  35
|
7 |   -  49

^
|_________________ 7x5 is the same as 5x7

Of all these, the only product between 30 and 40 is 35, so the prime
factors we must be looking for are 5 and 7, and the number is 35.

Does this make sense?

Your problem is like this, but with different numbers.  Can you use
the solution above as a model for solving your problem?

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

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