# #12: Highly divisible triangular number

The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:

Let us list the factors of the first seven triangle numbers:

```
1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28
```

We can see that 28 is the first triangle number to have over five divisors.

What is the value of the first triangle number to have over five hundred divisors?

# Python

```
def l_factors(x):
[ll, lh] = [[], []]
for f in range(1, int(x ** (1/2.0)) + 1):
if x % f == 0:
ll.append(f)
fp = x / f
if fp != f:
lh.append(int(fp))
return ll + list(reversed(lh))
tri = [2, 3]
while len(l_factors(tri[1])) < 500:
tri[0] += 1
tri[1] += tri[0]
ans = tri[1]
print(ans)
```

```
## 76576500
```