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
$\displaystyle 367200=100\cdot3762=10\cdot10\cdot9\cdot418$
collecting a few factors gives...
$\displaystyle 2^2\cdot3^2\cdot5^2\cdot418$
working on the 418
$\displaystyle 418=2\cdot209=2\cdot11\cdot19$
combing all of the work gives...
$\displaystyle 2^3\cdot3^2\cdot5^2\cdot11\cdot19$