Finding the Factors of a Number!

It really bothers me when things take way too much time to do. Especially when a calculator will make the task so much easier. I've started Chapter 2 in my Math book and it's all about fractions and what not. So I'm breezing along and all of a sudden I hit a brick wall. Ouch! It's not that I don't know how to do this it's just so tedious! I have to find the factors of any given number. It's pretty simple with a smaller number but when you get a number such as 3467 or something it's annoying. I found divisibility rules up to 20 that help out but factors after 20 I've been doing long division to find. Here are the divisibility rules that I have found up to 20:

2 – if it ends in 0, 2, 4, 6, or 8, it is an even number.
3 – if the sum of its digits are divisible by 3.
4 – if the last two digits make a number divisible by 4.
5 – if it ends in 0 or 5.
6 – if it is divisible by both 2 and 3.
7 – has no simple test.
8 – if the last three digits make a number divisible by 8.
9 – if the sum of the digits is divisible by 9.
10 – if it ends in zero.
11 – if the difference between the sum of the even numbers and the sum of the odd numbers is divisible by 11.
12 – if it is divisible by both 3 and 4.
13 – delete the last digit from the number, then subtract 9 times the deleted digit. If what is left is divisible by 13 then so is the number.
14 – if it is divisible by 2 and 7.
15 – if it is divisible by 3 and 5.
16 – has no simple test.
17 - subtract 5 times the last digit from the rest. If that number is divisible by 17 so is your number.
18 – if it is divisible by 2 and by 9.
19 – add two times the last digit to the rest. if that number is divisible by 19 so is your number.
20 – if it is divisible by 10, and the tens digit is even.

I haven't tested all of these yet so I'm hoping that they work. If anyone can tell me an easier way to do this please, please, please do because I have no clue. Besides the fact that this is annoying I am actually finding that I don't hate math as much as I thought.