Convert Integer to Hex String Without sprintf or itoa functions

Code

#include <stdio.h>
#include <stdint.h>

void print_hex(uint16_t num) {
    if (num == 0){
        printf("0");
        return;
    }

    char hex[] = "0123456789ABCDEF";
    char output[20];
    int index = 0;

    while(num){
        int remainder = num % 16;
        output[index++] = hex[remainder];
        num /= 16;
    }

    for (int i = index - 1; i >= 0; i--){
        putchar(output[i]);
    }

}

int main() {
    uint16_t num;
    scanf("%hu", &num);
    print_hex(num);
    return 0;
}

Solving Approach