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:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

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?

Solution:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

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?

Solution:

void Solution() { int i = 1; int triangleNumber = 0; do { triangleNumber = i * (i + 1) / 2; i++; } while (NoOfDivisors(triangleNumber) <= 500); Console.WriteLine(triangleNumber); } static int NoOfDivisors(int num) { //Based on the formula, otherwise it will take infinite time //Let d(n) be the number of divisors for the natural number, n. //We begin by writing the number as a product of prime factors: n = paqbrc... //then the number of divisors, d(n) = (a+1)(b+1)(c+1)... int counter = 0; int totalCount = 1; bool flag = false; int tempNum = num; for (int i = 2; i <= num / 2; i++) { if (tempNum % i == 0) { counter++; tempNum = tempNum / i; i--; flag = true; continue; } if (flag) { totalCount = totalCount * (counter + 1); counter = 0; flag = false; } if (tempNum == 1) break; } return totalCount; }