Find Generators of a fiel mod a prime number in C

Generator.c

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

// Function to compute (base^exp) % mod using fast modular exponentiation
long long mod_exp(long long base, long long exp, long long mod) {
    long long result = 1;
    while (exp > 0) {
        if (exp % 2 == 1) result = (result * base) % mod;
        base = (base * base) % mod;
        exp /= 2;
    }
    return result;
}

// Function to compute prime factors of n and store in factors[]
int prime_factors(int n, int factors[]) {
    int count = 0;
    while (n % 2 == 0) {
        if (count == 0) factors[count++] = 2;
        n /= 2;
    }
    for (int i = 3; i * i <= n; i += 2) {
        if (n % i == 0) {
            factors[count++] = i;
            while (n % i == 0) n /= i;
        }
    }
    if (n > 1) factors[count++] = n;
return count;
}

// Function to check if g is a generator mod p
int is_generator(int g, int p, int phi, int factors[], int num_factors) {
    for (int i = 0; i < num_factors; i++) {
        //printf("%3d %3d\n", g, phi / factors[i]);''
        long long result = mod_exp(g, phi / factors[i], p);
        //printf("|%3d,%3d,%3d| %d\n ", g, phi / factors[i],p, result);
        if (result== 1) return 0;
    }
    return 1;
}

// Function to find all generators mod p
void find_generators(int p) {
    int phi = p - 1;
    int factors[20]; // Enough to store prime factors
    int num_factors = prime_factors(phi, factors);
    
    printf("Generators of %d: ", p);
    for (int g = 2; g < p; g++) {
        if (is_generator(g, p, phi, factors, num_factors)) {
            printf("%d ", g);
        }
    }
    printf("\n");
}

int main() {
    int p = 13;
    find_generators(p);
    return 0;
}