79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
111 lines
2.6 KiB
Markdown
111 lines
2.6 KiB
Markdown
---
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id: 5900f39c1000cf542c50feae
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challengeType: 5
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title: 'Problem 47: Distinct primes factors'
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---
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## Description
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<section id='description'>
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The first two consecutive numbers to have two distinct prime factors are:
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<div style='padding-left: 4em;'>14 = 2 × 7</div>
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<div style='padding-left: 4em;'>15 = 3 × 5</div>
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The first three consecutive numbers to have three distinct prime factors are:
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<div style='padding-left: 4em;'>644 = 2² × 7 × 23</div>
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<div style='padding-left: 4em;'>645 = 3 × 5 × 43</div>
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<div style='padding-left: 4em;'>646 = 2 × 17 × 19</div>
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Find the first four consecutive integers to have four distinct prime factors each. What is the first of these numbers?
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>distinctPrimeFactors(2, 2)</code> should return 14.
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testString: assert.strictEqual(distinctPrimeFactors(2, 2), 14, '<code>distinctPrimeFactors(2, 2)</code> should return 14.');
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- text: <code>distinctPrimeFactors(3, 3)</code> should return 644.
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testString: assert.strictEqual(distinctPrimeFactors(3, 3), 644, '<code>distinctPrimeFactors(3, 3)</code> should return 644.');
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- text: <code>distinctPrimeFactors(4, 4)</code> should return 134043.
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testString: assert.strictEqual(distinctPrimeFactors(4, 4), 134043, '<code>distinctPrimeFactors(4, 4)</code> should return 134043.');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function distinctPrimeFactors(targetNumPrimes, targetConsecutive) {
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// Good luck!
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return true;
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}
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distinctPrimeFactors(4, 4);
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function distinctPrimeFactors(targetNumPrimes, targetConsecutive) {
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function isPrime(num) {
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for (let i = 2, s = Math.sqrt(num); i <= s; i++) {
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if (num % i === 0) {
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return false;
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}
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}
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return num !== 1;
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}
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function getPrimeFactors(num) {
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const factors = [];
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for (let i = 2; i <= Math.sqrt(num); i++) {
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if (num % i === 0) {
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// found a factor
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if (isPrime(i)) {
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factors.push(i);
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}
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if (isPrime(num / i) && i !== Math.sqrt(num)) {
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factors.push(num / i);
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}
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}
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}
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return factors;
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}
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function findConsecutiveNumbers() {
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let number = 0;
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let consecutive = 0;
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while (consecutive < targetConsecutive) {
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number++;
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if (getPrimeFactors(number).length >= targetNumPrimes) {
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consecutive++;
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} else {
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consecutive = 0;
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}
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}
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return (number - targetConsecutive) + 1;
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}
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return findConsecutiveNumbers();
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}
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```
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</section>
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