---
id: 5900f39c1000cf542c50feae
challengeType: 5
title: 'Problem 47: Distinct primes factors'
---
## Description
The first two consecutive numbers to have two distinct prime factors are:
14 = 2 × 7
15 = 3 × 5
The first three consecutive numbers to have three distinct prime factors are:
644 = 2² × 7 × 23
645 = 3 × 5 × 43
646 = 2 × 17 × 19
Find the first four consecutive integers to have four distinct prime factors each. What is the first of these numbers?
## Instructions
## Tests
```yml
tests:
- text: distinctPrimeFactors(2, 2) should return 14.
testString: assert.strictEqual(distinctPrimeFactors(2, 2), 14, 'distinctPrimeFactors(2, 2) should return 14.');
- text: distinctPrimeFactors(3, 3) should return 644.
testString: assert.strictEqual(distinctPrimeFactors(3, 3), 644, 'distinctPrimeFactors(3, 3) should return 644.');
- text: distinctPrimeFactors(4, 4) should return 134043.
testString: assert.strictEqual(distinctPrimeFactors(4, 4), 134043, 'distinctPrimeFactors(4, 4) should return 134043.');
```
## Challenge Seed
```js
function distinctPrimeFactors(targetNumPrimes, targetConsecutive) {
// Good luck!
return true;
}
distinctPrimeFactors(4, 4);
```
## Solution
```js
function distinctPrimeFactors(targetNumPrimes, targetConsecutive) {
function isPrime(num) {
for (let i = 2, s = Math.sqrt(num); i <= s; i++) {
if (num % i === 0) {
return false;
}
}
return num !== 1;
}
function getPrimeFactors(num) {
const factors = [];
for (let i = 2; i <= Math.sqrt(num); i++) {
if (num % i === 0) {
// found a factor
if (isPrime(i)) {
factors.push(i);
}
if (isPrime(num / i) && i !== Math.sqrt(num)) {
factors.push(num / i);
}
}
}
return factors;
}
function findConsecutiveNumbers() {
let number = 0;
let consecutive = 0;
while (consecutive < targetConsecutive) {
number++;
if (getPrimeFactors(number).length >= targetNumPrimes) {
consecutive++;
} else {
consecutive = 0;
}
}
return (number - targetConsecutive) + 1;
}
return findConsecutiveNumbers();
}
```