[Tutor] HOW DO I PYTHONIZE A BASICALLY BASIC PROGRAM?

[WM.]

# The natural numbers(natnum), under 1000, divisible by 3 or by 5 are to 
be added together.
natnum = 0
num3 = 0
num5 = 0
cume = 0
# The 'and' is the 15 filter; the 'or' is the 3 or 5 filter.
while natnum <= 999:
     num3 = natnum/3
     num5 = natnum/5
     if natnum - (num3 * 3) == 0 and natnum - (num5 * 5) == 0:
         cume = cume + natnum
     elif natnum - (num3 * 3) == 0 or natnum - (num5 * 5) == 0:
         if natnum - (num3 * 3) == 0:
             cume = cume + natnum
         elif natnum - (num5 * 5) == 0:
             cume = cume + natnum
     natnum = natnum + 1
print cume


This problem was kicked around last month and I did not understand any 
of the scripts.  So I tried to recall the BASIC ifs and loops. The 
project euler guys say it works, but how might it be made more Pythonic?