77599 ÷ 6 = 12933 R1
Alright, let's work through the division of 77599 by 6 step by step.

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

Step 2:
6 goes into 17 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 12
Subtract 12 from 17 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 6

Step 3:
6 goes into 55 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 129
Subtract 54 from 55 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 6

Step 4:
6 goes into 19 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 1293
Subtract 18 from 19 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 6

Step 5:
6 goes into 19 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 12933
Subtract 18 from 19 to get 1.

The final result is 12933 with a remainder of 1.