JavaScript/Project-Euler/Problem012.js at master · TheAlgorithms/JavaScript · GitHub

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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 }

JavaScript/Project-Euler/Problem012.js at master · TheAlgorithms/JavaScript · GitHub

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JavaScript/Project-Euler/Problem012.js at master · TheAlgorithms/JavaScript · GitHub

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