36778 ÷ 6 = 6129 R4
Let's divide 36778 by 6.

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 (6) of the dividend behind the 3 and repeat the process: 36 / 6

Step 2:
6 goes into 36 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 36 from 36 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 6

Step 3:
6 goes into 7 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 61
Subtract 6 from 7 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 6

Step 4:
6 goes into 17 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 612
Subtract 12 from 17 to get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 6

Step 5:
6 goes into 58 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 6129
Subtract 54 from 58 to get 4.

The final result is 6129 with a remainder of 4.