34979 ÷ 8 = 4372 R3
Alright, let's work through the division of 34979 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 (4) of the dividend behind the 3 and repeat the process: 34 / 8

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

Step 3:
8 goes into 29 3 times with a remainder of 5.
Write down 3 as next digit of of the result. 
Result so far: 43
Subtract 24 from 29 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 8

Step 4:
8 goes into 57 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 437
Subtract 56 from 57 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 8

Step 5:
8 goes into 19 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 4372
Subtract 16 from 19 to get 3.

The final result is 4372 with a remainder of 3.