Project Euler - Problem 3 - Largest prime factor
What is the largest prime factor of the given number?
The problem
This is problem 3 from the Project Euler.
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the given number?
First of all, what is a prime number?
According to Wikipedia:
prime numbers are the natural numbers greater than one that are not products of two smaller natural numbers.
And from Fact Monster:
A prime number can be divided, without a remainder, only by itself and by 1. For example, 17 can be divided only by 17 and by 1.
Let’s begin
Initialise variables and common functions:
// list of numbers we wanna test
var test_values = [2, 3, 5, 7, 13195, 600851475143];
// this function execute the code and records the time to execute
function run_function(func, test_values) {
for(var i in test_values){
console.log('Test value:', test_values[i]);
var t0 = performance.now();
console.log('Output:', func(test_values[i]));
var t1 = performance.now();
console.log("Took " + (t1 - t0) + " ms");
console.log();
}
}
Attempt #1: for-loop, divide number check reminder
Since all even numbers can be divided by 2, we shall return 2 for every even input number. That’s the easy part.
When the input number is an odd number, we need to do some division to check for whole numbers.
A prime number cannot be formed by multiplying two smaller whole numbers, so we divide the odd numbers i to check if the division produces any reminder (decimal values).
If dividing odd number i result in a value with a reminder, i is not a prime number to the input number.
If dividing odd number i is a whole number, then i is one of the prime numbers for input number.
function largestPrimeFactor(number) {
// only even prime number is 2. All other even numbers can be divided by 2.
if(number%2===0){
return 2;
}
// test the odd numbers, greater than 3
var list_of_prime_numbers = [];
var i = 3;
// check the division of the input number and i variable
// if division no reminder, it is one of the prime numbers
// if not, increase i by 2 to test the next odd number
while(number != 1){
if(number % i === 0){
number /= i;
list_of_prime_numbers.push(i);
}else{
i+=2; // increase by 2 to test the next odd number
}
}
// return the last prime value
return list_of_prime_numbers[list_of_prime_numbers.length-1];
}
run_function(largestPrimeFactor, test_values);
The output:
Test value: 2
Output: 2
Took 0.0949999998738349 ms
Test value: 3
Output: 3
Took 0.019999999949504854 ms
Test value: 5
Output: 5
Took 0.06500000017695129 ms
Test value: 7
Output: 7
Took 0.030000000151630957 ms
Test value: 13195
Output: 29
Took 0.02500000027794158 ms
Test value: 600851475143
Output: 6857
Took 0.2799999997478153 ms
Here’s my solution, can it be any better?
This is my Project Euler Challenge journey; anyone wants to do this together? It will be fun and we can learn a thing or two by solving this problem in different ways.