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Prime Number Length

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by exhilaration » Sat May 30, 2009 8:34 pm
Hi guys...

How many different two digit positive integers have a length of six? Length is defined as the number of prime factors, e.g., 75 = 5*5*3, has a length of three.

Thanks...
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by raleigh » Sat May 30, 2009 8:40 pm
Let's start by seeing what the smallest number with length six can look like:

2*2*2*2*2*2 = 64

Now let's start incrementing factors and see what we get.

2*2*2*2*2*3 = 32*3 = 96

Luckily, the initial investigation went a long way. If we increment another 2 to 3, that will be over 100. Also, if we increment a 2 to 5 instead of 3, that will be over 100 as well.

The answer is two.
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by exhilaration » Sat May 30, 2009 8:50 pm
raleigh wrote:Let's start by seeing what the smallest number with length six can look like:

2*2*2*2*2*2 = 64

Now let's start incrementing factors and see what we get.

2*2*2*2*2*3 = 32*3 = 96

Luckily, the initial investigation went a long way. If we increment another 2 to 3, that will be over 100. Also, if we increment a 2 to 5 instead of 3, that will be over 100 as well.

The answer is two.
Wicked, thanks buddy.
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