The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

We neeed to find the largest prime factor of 600851475143.

We know that the largest prime factor of a number, its the number itself.

As a concept refresher, any prime number is only divisible by 1 ant itself, thus, when dividing by a certain number, there should not be a reminder.

2 is the first prime number, and holds the honor of being the only even prime numnber.

We’ll start by making a function to return a `bool` if the former condition holds.

``````func isPrime(x
int64) bool {
var i int64 = 2 // We start with 2 as it is the first prime number

for ; i < x; i++ {
if x % i == 0 {
return false
}
}

return true
}

``````

Next, we need to test factors and see if they are prime numbers. Let’s state:

\$\$ ab = N space where space 1 < a leq b leq N \$\$

\$\$ N = ab geq a^2 Leftrightarrow a^2 leq N Rightarrow sqrt[]{N} \$\$

This means that in order to test the primality of a composite number N, you check if this number is a product of two numbers. Thus we use square root.

``````package main

import (
"fmt"
"math"
"time"
)

const n int64 = 600851475143

func isPrime(x int64) bool {
var i int64 = 2
for i < x; i++ {
if x%i == 0 {
return false
}
}
return true
}

func
main() {
start := time.Now()
var i = int64(math.Sqrt(float64(n)))
for ;
i > 1; i-- {
if n % i == 0 && isPrime(i) {
fmt.Println("Execution time: ", time.Since(start))
fmt.Println("Largest Prime Factor: ", i)
break
}
}
}

``````

Execution time: 7.990898ms