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import PIL
import math
# Problem 12 Highly divisible triangular number
# finds the first number with over 500 factors
def countfactors(num):
factors = 0
# we only need to know about the FIRST HALF of factors,
# one factor implies a second
root = int(math.ceil(math.sqrt(num)))
divs = range(1, root)
for d in divs:
if(num % d == 0):
factors += 2
# Correction if the number is a perfect square
if (root * root == num):
factors -= 1
return factors
#### MAIN #####
i = 1
k = 1
j = 0
while(k < 500):
j += i
k = countfactors(j)
print(str(j) + " has " + str(k) + " factors")
i += 1
print("Ding! Ding! {} has over 500 factors, wow!".format(j))
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