Project Euler Solution 3

Problem Statement#

Find the largest prime factor of a composite number.

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

What is the largest prime factor of the number 600851475143 ?

Solution#

Whatever the problem is, first try to solve them manually and think how you solved it. Now try to write it down in a paper and then solve it using any programming language. That makes the program very simple, allows you to make changes when required and saves time that is required for programming.

The given larger number may be a prime number. So first check if the number is prime.

If the number is a perfect square: Example if number=36

36 = 6X6 = (2X3) X (2X3)

It is enough to calculate the largest prime factor of 6.

Let us see how to find out the prime factors of 13195

13195: Square Root(13195) ≈ 114

i = 2 to 114	2	3	4	5	6	7	-	-	114
number = 13195	13195%2 != 0	13195%3 != 0	13195%4 != 0	13195%5 = 0 13195/5 = 2639	-	-	-	-	-

2639: Square root(2639) ≈ 51

i = 2 to 51	2	3	4	5	6	7	-	-	51
number = 2639	2639%2 != 0	2639%3 != 0	2639%4 != 0	2639%5 != 0	2639%6 != 0	2639%7 = 0 2639/7 = 377	-	-	-

377: Square root(377) ≈ 19

i = 2 to 19	2	3	4	-	-	13	-	-	19
number = 377	377%2 != 0	377%3 != 0	377%4 != 0	-	-	377%13 = 0 377/13 = 29	-	-	-

29: Square root(29) ≈ 5

i = 2 to 5	2	3	4	5
number = 29	29%2 != 0	29%3 != 0	29%4 != 0	29%5 != 0

29 is not divisible by any numbers from 2 to 5, so 29 is the largest prime factor of 13195.

Implementation#

#include <stdio.h>#include <math.h>
long long int number = 600851475143;int i, sq_no;int isPrime(long long int);
int main(){    if (isPrime(number))    {        printf("%d is a prime number", number);        return 0;    }    while (number != 1)    {
        sq_no = floor(sqrt(number));        if (isPrime(number))        {            printf("%d", number);            return 0;        }        for (i = 2; i <= sq_no; i++)        {            if ((number % i) == 0)            {                number = number / i;                break;            }        }        if (number == 2 || number == 3)        {            printf("%d", number);            return 0;        }    }    return 0;}
int isPrime(long long int num){    int j, num_sqrt;    num_sqrt = sqrt(num);    if (num == num_sqrt *num_sqrt) return 0;    for (j = 2; j <= num_sqrt; j++)        if ((num % j) == 0) return 0;    return 1;}

Sample Output#

Sample Output