Factors

Factors

If:

N = p^a * q^b * r^c

Then:

Number of factors = (a+1)(b+1)(c+1)
Sum of factors = [(p^(a+1)-1)/(p-1)] * [(q^(b+1)-1)/(q-1)] * ...
Product of factors = N^(number of factors / 2)

Perfect square:

All prime powers are even.
Number of factors is odd.

Trailing zeroes:

Trailing zeroes = number of pairs of 2 and 5
Usually count 5s, since 2s are more frequent.