Although Euler Project questions are designed to be solved sequentially. I wasn’t able to hold myself from giving it a try when I saw some of my roommates trying out this problem.
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:
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?
I tried out the above problem and got myself a solution using two basic rules from mathematics.
- The nth triangular number can easily be obtained as : (n * n-1) / 2
- If a number ” n ” can be written as a multiple of two consecutive numbers “p” and “q” ie: if n = p * q then number of factors of n = number of factors of p * number of factors of q – 1
My Solution is available at my git-hub id:
My solution clocked below 1 seconds.( 0.244 seconds to be exact ) .