12737 ÷ 6 = 2122 R5
Alright, let's work through the division of 12737 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 (2) of the dividend behind the 1 and repeat the process: 12 / 6

Step 2:
6 goes into 12 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 12 from 12 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: 21
Subtract 6 from 7 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 6

Step 4:
6 goes into 13 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 212
Subtract 12 from 13 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: 2122
Subtract 12 from 17 to get 5.

The final result is 2122 with a remainder of 5.