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I have to write this in an open ended response!
There's how you might write a computer program to do it; and then how a human being does it. Which do you want?
Uhm... The answer!
Well, evaluate honestly how you do it. For example, if I asked you for the prime factorization of 720, how would you figure it out?
easier one then. What's the prime factorization of 100?
excuse interruption - i answered your lcm question agbyoung
i do it like steve jobs http://www.wolframalpha.com/input/?i=factor+264575
jimmyrep could you answer this one to?
pick a number. then factor. that is what you have to do, there is no shortcut
the way i do it is as follows ; if its even divide by 2 if not try 3 if it ends in 5 - try 5 7 etc example: factorise 2360: 2 ) 2360 2 ) 1180 2 ) 590 2 ) 295 5 ) 59 59 is a prime number so 1260 = 2x2x2x2x5x59 or 2^4*5*59
i pick 72 \[72=2\times 36=2\times 2\times 18=2\times 2\times 2\times 9=2\times 2\times 2\times 3\times 3=2^3\times 3^2\]
\[ 100 = 10^2 = (2 \times 5)^2 = 2^2 \times 5^2 \]
The way I would actually do 2360 is a little differently; not better or worse, just different. First I'd pull out the 10. Then I see 236 is divisible by 4, so I have \[ 2360 = 10 \times 4 \times 59 \] Now 59 is prime so now I have \[ 2360 = (2 \times 5) \times (2 \times 2) \times 59 = 2^3 \times 5 \times 59 \] (which IS different from Jimmy's answer, because his is not quite correct.)
If I were writing a computer program, I'd implement an algorithm like jimmy's
hhmm - oh yes - I put in one 2 too many !!!