CS50 Week1: credit task improvements? - c

Question

First up: i got no prior coding experience and took nearly the whole day to do this task with only the tools they gave us in the first week.
I actually managed to do it, but the code looks not pretty and i want to see if i can improve it somehow?
How could i make the Luhn-algorithm more elegant or the boolean logic at the end (see the Mastercard OR orgy) ?
I would appreciate any help :)
#include <stdio.h>
#include <cs50.h>
int main(void)
{
long num = get_long("Number: ");
int sum_eo, sum_no;
// determine length of input
int length = 0;
for (long i = 1; i < num; i *= 10)
{
length++;
}
// determine the first two numbers of the input
long start_digits = num;
for (int i = 0; i < (length - 2); i++)
{
start_digits /= 10;
}
// Luhn-algorithm
// first every other number from the back
for (long i = 100; i < (num * 10); i = i*100)
{
int every_other = (((num % i)- (num % (i / 10))) / (i/10));
if ((every_other * 2) < 10)
{
sum_eo = sum_eo + (every_other * 2);
}
else
{
sum_eo = sum_eo + 1 + ((every_other*2) % 10);
}
}
// then the other numbers
for (long i = 10; i < (num * 10); i = i*100)
{
int every_no = (((num % i)- (num % (i / 10))) / (i/10));
sum_no = sum_no + every_no;
}
//calculate checksum and choose which card
int checksum = (sum_eo + sum_no) % 10;
if (checksum == 0) //
{
if (length == 15 && (start_digits == 34 || start_digits == 37))
{
printf("AMEX\n");
}
else if ((length == 13 || length == 16) && (start_digits / 10) == 4)
{
printf("VISA\n");
}
else if (length == 16 && (start_digits == 51 || start_digits == 52 || start_digits == 53 || start_digits == 54 || start_digits == 55))
{
printf("MASTERCARD\n");
}
else
printf("INVALID\n");
}
else
printf("INVALID\n");
}

Answer 1

One potential change that you can make is here:
else if (length == 16 && (start_digits == 51 || start_digits == 52 || start_digits == 53 || start_digits == 54 || start_digits == 55))
you can instead do this:
else if (length == 16 && (start_digits >= 51 && start_digits <= 55))