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import PIL, math
import numpy as np
#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
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