The Amazing 2592

A friend (it was Sean) pointed this out to me today:

Consider the amazing number 2592.  Why is it so amazing?  Well, factor it.  It’s even, so you can divide by 2 to get:

2592 = 2\times1296

Oh, we can factor out another 2:

2592 = 2^2\times648

And another 2:

2592 = 2^3\times324

Again:

2592 = 2^4\times162

Yet, again:

2592 = 2^5\times 81

Finally, we’ve factored out all of the 2’s there are. and since 81=9^2 we have:

2592 = 2^5\times9^2

Or, if we indicate the multiplication by writing the numbers next to each other:

2592=2^59^2

See what I’m saying? Amazing! Can you find any other numbers that behave like this? I tried a little today to find any and wasn’t successful, but let me know if you find any.

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2 Responses to The Amazing 2592

  1. Slavka says:

    That’s cool! I’m going to share it with Ryan- who has been doing a ton of factoring lately.

  2. Prakash says:

    wow cool… Plz post more such stuffs….

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