Challenge Level

Each number will appear as a factor in 100!. So, for example
100! = 100x99x98x...where 2^{2}is a factor of 100, 2 is a
factor of 98 and 2^{5} is a factor of 96. Are there
patterns to the powers of the number that appear as you consider
each term of the factorial? Can this pattern be generalised for
other numbers?