35366 ÷ 4 = 8841 R2
Let's divide 35366 by 4.

Step 1:
4 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 (5) of the dividend behind the 3 and repeat the process: 35 / 4

Step 2:
4 goes into 35 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 32 from 35 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 4

Step 3:
4 goes into 33 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 88
Subtract 32 from 33 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 4

Step 4:
4 goes into 16 4 times with a remainder of 0.
Write down 4 as next digit of of the result. 
Result so far: 884
Subtract 16 from 16 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 4

Step 5:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 8841
Subtract 4 from 6 to get 2.

The final result is 8841 with a remainder of 2.