35498 ÷ 8 = 4437 R2
Alright, let's work through the division of 35498 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 (4) of the dividend behind the 3 and repeat the process: 34 / 8

Step 3:
8 goes into 34 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 44
Subtract 32 from 34 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 8

Step 4:
8 goes into 29 3 times with a remainder of 5.
Write down 3 as next digit of of the result. 
Result so far: 443
Subtract 24 from 29 to get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 8

Step 5:
8 goes into 58 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 4437
Subtract 56 from 58 to get 2.

The final result is 4437 with a remainder of 2.