73653 ÷ 6 = 12275 R3
Alright, let's work through the division of 73653 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 (3) of the dividend behind the 1 and repeat the process: 13 / 6

Step 2:
6 goes into 13 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 12
Subtract 12 from 13 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 6

Step 3:
6 goes into 16 2 times with a remainder of 4.
Write down 2 as next digit of of the result. 
Result so far: 122
Subtract 12 from 16 to get 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 6

Step 4:
6 goes into 45 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 1227
Subtract 42 from 45 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 6

Step 5:
6 goes into 33 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 12275
Subtract 30 from 33 to get 3.

The final result is 12275 with a remainder of 3.