# Math Help - prime power decomp

1. ## prime power decomp

I'm having trouble with prime power decomposition! I'm sure it's quite simple, but i just can't wrap my brain around it!

for example, what is the prime power decomposition of 367200?

2. Originally Posted by dancer17
I'm having trouble with prime power decomposition! I'm sure it's quite simple, but i just can't wrap my brain around it!

for example, what is the prime power decomposition of 367200?
we want to break it up into prime factors so

$367200=100\cdot3762=10\cdot10\cdot9\cdot418$

collecting a few factors gives...

$2^2\cdot3^2\cdot5^2\cdot418$

working on the 418

$418=2\cdot209=2\cdot11\cdot19$

combing all of the work gives...

$2^3\cdot3^2\cdot5^2\cdot11\cdot19$