13623 ÷ 6 = 2270 R3
We're going to perform division on 13623 with 6 as the divisor.

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 (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: 2
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: 22
Subtract 12 from 16 to get 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 6

Step 4:
6 goes into 42 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 227
Subtract 42 from 42 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 6

Step 5:
6 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 2270
Subtract 0 from 3 to get 3.

The final result is 2270 with a remainder of 3.