76493 ÷ 6 = 12748 R5
Alright, let's work through the division of 76493 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 (6) of the dividend behind the 1 and repeat the process: 16 / 6

Step 2:
6 goes into 16 2 times with a remainder of 4.
Write down 2 as next digit of of the result. 
Result so far: 12
Subtract 12 from 16 to get 4.
Bring next digit (4) of the dividend behind the 4 and repeat the process: 44 / 6

Step 3:
6 goes into 44 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 127
Subtract 42 from 44 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 6

Step 4:
6 goes into 29 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 1274
Subtract 24 from 29 to get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 6

Step 5:
6 goes into 53 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 12748
Subtract 48 from 53 to get 5.

The final result is 12748 with a remainder of 5.