35276 ÷ 8 = 4409 R4
Alright, let's work through the division of 35276 by 8 step by step.

Step 1:
8 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 / 8

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

Step 3:
8 goes into 32 4 times with a remainder of 0.
Write down 4 as next digit of of the result. 
Result so far: 44
Subtract 32 from 32 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 8

Step 4:
8 goes into 7 0 times with a remainder of 7.
Write down 0 as next digit of of the result. 
Result so far: 440
Subtract 0 from 7 to get 7.
Bring next digit (6) of the dividend behind the 7 and repeat the process: 76 / 8

Step 5:
8 goes into 76 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 4409
Subtract 72 from 76 to get 4.

The final result is 4409 with a remainder of 4.