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---
id: 5900f3781000cf542c50fe8b
title: 'Problem 12: Highly divisible triangular number'
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challengeType: 5
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forumTopicId: 301746
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dashedName: problem-12-highly-divisible-triangular-number
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---
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# --description--
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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:
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< div style = 'text-align: center;' > 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...< / div >
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Let us list the factors of the first seven triangle numbers:
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< div style = 'padding-left: 4em;' > < b > 1:< / b > 1< / div >
< div style = 'padding-left: 4em;' > < b > 3:< / b > 1, 3< / div >
< div style = 'padding-left: 4em;' > < b > 6:< / b > 1, 2, 3, 6< / div >
< div style = 'padding-left: 4em;' > < b > 10:< / b > 1, 2, 5, 10< / div >
< div style = 'padding-left: 4em;' > < b > 15:< / b > 1, 3, 5, 15< / div >
< div style = 'padding-left: 4em;' > < b > 21:< / b > 1, 3, 7, 21< / div >
< div style = 'padding-left: 4em;' > < b > 28:< / b > 1, 2, 4, 7, 14, 28< / div >
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We can see that 28 is the first triangle number to have over five divisors.
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What is the value of the first triangle number to have over `n` divisors?
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# --hints--
`divisibleTriangleNumber(5)` should return a number.
```js
assert(typeof divisibleTriangleNumber(5) === 'number');
```
`divisibleTriangleNumber(5)` should return 28.
```js
assert.strictEqual(divisibleTriangleNumber(5), 28);
```
`divisibleTriangleNumber(23)` should return 630.
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```js
assert.strictEqual(divisibleTriangleNumber(23), 630);
```
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`divisibleTriangleNumber(167)` should return 1385280.
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```js
assert.strictEqual(divisibleTriangleNumber(167), 1385280);
```
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`divisibleTriangleNumber(374)` should return 17907120.
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```js
assert.strictEqual(divisibleTriangleNumber(374), 17907120);
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```
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`divisibleTriangleNumber(500)` should return 76576500.
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```js
assert.strictEqual(divisibleTriangleNumber(500), 76576500);
```
# --seed--
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## --seed-contents--
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```js
function divisibleTriangleNumber(n) {
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return true;
}
divisibleTriangleNumber(500);
```
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# --solutions--
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```js
function divisibleTriangleNumber(n) {
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if (n === 1) return 3;
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let counter = 1;
let triangleNumber = counter++;
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while (noOfFactors(triangleNumber) < n ) {
triangleNumber += counter++;
}
return triangleNumber;
}
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function noOfFactors(num) {
const primeFactors = getPrimeFactors(num);
let prod = 1;
for(let p in primeFactors) {
prod *= (primeFactors[p] + 1)
}
return prod;
}
function getPrimeFactors(num) {
let n = num;
let primes = {};
let p = 2;
let sqrt = Math.sqrt(num);
function checkAndUpdate(inc) {
if (n % p === 0) {
const curr = primes[p];
if (curr) {
primes[p]++
} else {
primes[p] = 1;
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}
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n /= p;
} else {
p += inc;
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}
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}
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while(p === 2 & & p < = n) {
checkAndUpdate(1);
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}
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while (p < = n & & p < = sqrt) {
checkAndUpdate(2);
}
if(Object.keys(primes).length === 0) {
primes[num] = 1;
} else if(n !== 1) {
primes[n] = 1;
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}
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return primes;
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}
```