Project Euler Problem 12 Solved   2014-03-28


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:

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

p12.go
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package main

import (
"fmt"
"math"
)

func count_divisor(num int64) int64 {
var count, factor, lastFactor, exponent int64 = 1, 2, 0, 1

for factor <= num {
if math.Mod(float64(num), float64(factor)) == 0 {
if factor == lastFactor {
exponent++
} else {
count *= (exponent + 1)
exponent = 1
lastFactor = factor
}
num /= factor
} else {
factor++
}
}

return count
}

func main() {
var count, n int64 = 0, 1
for count < 500 {
n++
count = count_divisor(n * (n + 1) / 2)
}
fmt.Println(n*(n+1)/2, count)
}

I’m the 99509th person to have solved this problem.


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Contents

  1. Highly divisible triangular number
  2. Solution