Euler 12 need optimization - python-3.x

Question

I have solved euler problem 12, but it needs some optimization. I have read on the euler forums, but it has not helped me optimized it. However, I have managed to get the solution, I just need to speed it up. It currently takes 4 minutes to run. Here is my code:
import time
def nthtriangle(n):
return (n * (n + 1)) / 2
def numberofnfactors(n):
count = 0
if n==1:
return 1
for i in range(1, 1 + int(n ** 0.5)):
if n % i == 0:
count += 2
return count
def FirstTriangleNumberWithoverxdivisors(divisors):
found = False
counter = 1
while not found:
print(int(nthtriangle(counter)), " ", numberofnfactors(nthtriangle(counter)))
if numberofnfactors(nthtriangle(counter)) > divisors:
print(" first triangle with over ",divisors, " divisors is ", int(nthtriangle(counter)))
found = True
break
counter += 1
start_time = time.time()
FirstTriangleNumberWithoverxdivisors(500)
print("My program took", time.time() - start_time, "to run")

Answer 1

Instead of calculating each triangle number individually, use a generator to get the triangle numbers
from timeit import timeit
def triangle_numbers():
count = 1
num = 0
while True:
num += count
count += 1
yield num
def count_divisors(n):
count = 0
if n==1:
return 1
for i in range(1, 1 + int(n ** 0.5)):
if n % i == 0:
count += 2
return count
print(timeit('next(num for num in triangle_numbers() if count_divisors(num) >= 500)',
globals=globals(), number=1))
Gives me 3.8404819999996107 (seconds) on my machine. You could probably also improve the divisor counting.
What's really slowing you down is calling nthtriangle and numberoffactors more than once in your loop! Plus, those calls to print aren't free.