3637 ÷ 9 = 404 R1
Alright, let's work through the division of 3637 by 9 step by step.

Step 1:
9 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 9

Step 2:
9 goes into 36 4 times with a remainder of 0.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 36 from 36 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 9

Step 3:
9 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 40
Subtract 0 from 3 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 9

Step 4:
9 goes into 37 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 404
Subtract 36 from 37 to get 1.

The final result is 404 with a remainder of 1.