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Problem012.js
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64 lines (60 loc) · 1.87 KB
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/**
* Problem 12 - Highly divisible triangular number
*
* https://projecteuler.net/problem=11
*
* 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?
*/
/**
* Gets number of divisors of a given number
* @params num The number whose divisors to find
*/
const getNumOfDivisors = (num) => {
// initialize numberOfDivisors
let numberOfDivisors = 0
// if one divisor less than sqrt(num) exists
// then another divisor greater than sqrt(n) exists and its value is num/i
const sqrtNum = Math.sqrt(num)
for (let i = 0; i <= sqrtNum; i++) {
// check if i divides num
if (num % i === 0) {
if (i === sqrtNum) {
// if both divisors are equal, i.e., num is perfect square, then only 1 divisor
numberOfDivisors++
} else {
// 2 divisors, one of them is less than sqrt(n), other greater than sqrt(n)
numberOfDivisors += 2
}
}
}
return numberOfDivisors
}
/**
* Loops till first triangular number with 500 divisors is found
*/
const firstTriangularWith500Divisors = () => {
let triangularNum
// loop forever until numOfDivisors becomes greater than or equal to 500
for (let n = 1; ; n++) {
// nth triangular number is (1/2)*n*(n+1) by Arithmetic Progression
triangularNum = (1 / 2) * n * (n + 1)
if (getNumOfDivisors(triangularNum) >= 500) return triangularNum
}
}
export { firstTriangularWith500Divisors }