17787 ÷ 6 = 2964 R3
Alright, let's work through the division of 17787 by 6 step by step.

Step 1:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 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: 2
Subtract 12 from 17 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 6

Step 3:
6 goes into 57 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 29
Subtract 54 from 57 to get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 6

Step 4:
6 goes into 38 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 296
Subtract 36 from 38 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 6

Step 5:
6 goes into 27 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 2964
Subtract 24 from 27 to get 3.

The final result is 2964 with a remainder of 3.