## 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.