33977 ÷ 6 = 5662 R5
Alright, let's work through the division of 33977 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 (3) of the dividend behind the 3 and repeat the process: 33 / 6

Step 2:
6 goes into 33 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 30 from 33 to get 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 6

Step 3:
6 goes into 39 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 56
Subtract 36 from 39 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 6

Step 4:
6 goes into 37 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 566
Subtract 36 from 37 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 6

Step 5:
6 goes into 17 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 5662
Subtract 12 from 17 to get 5.

The final result is 5662 with a remainder of 5.