So lets just go ahead and do 22 to base 4

1.) Make a base 10 chart ( not neccesary but it helps visualize the numbers more accuratley) Let * mean to the power of

10*2–10*1–10*0
100 10 1
2 2

2.)Make a Base 4 Chart (Note that you only have to find base 4 factors up to 22…for instance finding the value for 4*6=4096 is a waste of time as you wont be using that number for anything)

4*3–4*2–4*1–4*0
64 16 4 1

now you are going to divide.

3.) Start with 64…how many times does 64 go into 22…none so place a zero to hold the palce value.

4*3–4*2–4*1–4*0
64 16 4 1
0

4.)Now how many 16’s can go into 22? 1. so place a one

4*3–4*2–4*1–4*0
64 16 4 1
0 1

22-16=6 now instead of finding factors that go into 22, you must find the factors that go into 6.

5.) How many 4’s go into 6? 1!! place a one

4*3–4*2–4*1–4*0
64 16 4 1
0 1 1

Now subtract to get your last value. 6-4=2

6.) 4*3–4*2–4*1–4*0
64 16 4 1
0 1 1 2

7.) AWNSER!!!!! 112 in base 4

I hope this helped everyone as much as it has helped me!! Once you get the hang of it it takes only a few minutes to solve.