13814 ÷ 6 = 2302 R2
Let's divide 13814 by 6.

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 (8) of the dividend behind the 1 and repeat the process: 18 / 6

Step 3:
6 goes into 18 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 23
Subtract 18 from 18 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 6

Step 4:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 230
Subtract 0 from 1 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 6

Step 5:
6 goes into 14 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 2302
Subtract 12 from 14 to get 2.

The final result is 2302 with a remainder of 2.