Problem
https://projecteuler.net/problem=12
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?
Answer: 76576500
Solution
#include <iostream>
#include <cstdint>
using namespace std;
uint64_t largest_prime_factor(uint64_t number)
{
uint64_t answer = 1;
uint64_t point = 3;
uint64_t divisor = number;
while ( 0 == (divisor % 2)) {
answer = 2;
divisor = divisor/2;
}
while (divisor != 1) {
while ( 0 == (divisor % point)) {
answer = point;
divisor = divisor/point;
}
point += 2;
}
return answer;
}
#if ! defined UNITTEST_MODE
int main(int argc, char const *argv[])
{
std::cout << "Answer: " << largest_prime_factor(600851475143) << std::endl;
}
#endif // #if ! defined UNITTEST_MODE