static void Main(string[] args) {
    var number = int.Parse(args[0]);
    var count = 0;
    for (var cursor = number; cursor != 0 && cursor % 10 == 0; count++, cursor /= 10) { }
    Console.WriteLine($"Trailing zeros in {number}: {count}");
}

[etki@varmint Playground.SCD]$ bin/Debug/netcoreapp3.1/linux-x64/publish/Playground.SCD 12
Trailing zeros in 12: 0
[etki@varmint Playground.SCD]$ bin/Debug/netcoreapp3.1/linux-x64/publish/Playground.SCD 10000
Trailing zeros in 10000: 4
[etki@varmint Playground.SCD]$ bin/Debug/netcoreapp3.1/linux-x64/publish/Playground.SCD 130
Trailing zeros in 130: 1
[etki@varmint Playground.SCD]$ bin/Debug/netcoreapp3.1/linux-x64/publish/Playground.SCD 0
Trailing zeros in 0: 0

[etki@varmint Playground.SCD]$ bin/Debug/netcoreapp3.1/linux-x64/publish/Playground.SCD 010130
Trailing zeros in 10130: 1

static int TrailingZeros(int number) {
    var count = 0;
    
    while (number != 0 && number % 10 == 0) {
        number = number / 10;
        count++;
    }

    return count;
}