multiplication using arrays

// basic idea is how would you multiply two number on paper

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    public static List<int> Function(string N, int n)
    {
        var num = N.ToCharArray().ToList()
                   .Select(s => Convert
                   .ToInt32(s.ToString()))
                   .ToList();
        num.Reverse();

        // initially remainder is 0
        var remainder = 0;
        for (int i = 0; i < num.Count; i++)
        {
            var temp = num[i] * n + remainder;
            var inString = temp.ToString();

            if (inString.Length > 1)
            {
                num[i] = Convert.ToInt32(inString[1].ToString());
                remainder = Convert.ToInt32(inString[0].ToString());
            }
            else
            {
                num[i]= Convert.ToInt32(inString[0].ToString());
                remainder = 0;
            }
        }
        if(remainder!=0)
        {
            num.Add(remainder);
        }
        num.Reverse();
        return num;
    }