35879 ÷ 6 = 5979 R5
Alright, let's work through the division of 35879 by 6 step by step.

Step 1:
6 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 / 6

Step 2:
6 goes into 35 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 30 from 35 to get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 6

Step 3:
6 goes into 58 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 59
Subtract 54 from 58 to get 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 6

Step 4:
6 goes into 47 7 times with a remainder of 5.
Write down 7 as next digit of of the result. 
Result so far: 597
Subtract 42 from 47 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 6

Step 5:
6 goes into 59 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 5979
Subtract 54 from 59 to get 5.

The final result is 5979 with a remainder of 5.