17634 ÷ 4 = 4408 R2
Alright, let's work through the division of 17634 by 4 step by step.

Step 1:
4 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 4

Step 2:
4 goes into 17 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 16 from 17 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 4

Step 3:
4 goes into 16 4 times with a remainder of 0.
Write down 4 as next digit of of the result. 
Result so far: 44
Subtract 16 from 16 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 4

Step 4:
4 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 440
Subtract 0 from 3 to get 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 4

Step 5:
4 goes into 34 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 4408
Subtract 32 from 34 to get 2.

The final result is 4408 with a remainder of 2.