2.4 KiB
2.4 KiB
id | challengeType | title | forumTopicId |
---|---|---|---|
5900f39c1000cf542c50feae | 5 | Problem 47: Distinct primes factors | 302145 |
Description
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
tests:
- text: <code>distinctPrimeFactors(2, 2)</code> should return 14.
testString: assert.strictEqual(distinctPrimeFactors(2, 2), 14);
- text: <code>distinctPrimeFactors(3, 3)</code> should return 644.
testString: assert.strictEqual(distinctPrimeFactors(3, 3), 644);
- text: <code>distinctPrimeFactors(4, 4)</code> should return 134043.
testString: assert.strictEqual(distinctPrimeFactors(4, 4), 134043);
Challenge Seed
function distinctPrimeFactors(targetNumPrimes, targetConsecutive) {
// Good luck!
return true;
}
distinctPrimeFactors(4, 4);
Solution
function distinctPrimeFactors(targetNumPrimes, targetConsecutive) {
function numberOfPrimeFactors(n) {
let factors = 0;
// Considering 2 as a special case
let firstFactor = true;
while (n % 2 == 0) {
n = n / 2;
if (firstFactor) {
factors++;
firstFactor = false;
}
}
// Adding other factors
for (let i = 3; i < Math.sqrt(n); i += 2) {
firstFactor = true;
while (n % i == 0) {
n = n / i;
if (firstFactor) {
factors++;
firstFactor = false;
}
}
}
if (n > 1) { factors++; }
return factors;
}
let number = 0;
let consecutive = 0;
while (consecutive < targetConsecutive) {
number++;
if (numberOfPrimeFactors(number) >= targetNumPrimes) {
consecutive++;
} else {
consecutive = 0;
}
}
return number - targetConsecutive + 1;
}