13877 ÷ 9 = 1541 R8
Let's divide 13877 by 9.

Step 1:
9 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 / 9

Step 2:
9 goes into 13 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 9 from 13 to get 4.
Bring next digit (8) of the dividend behind the 4 and repeat the process: 48 / 9

Step 3:
9 goes into 48 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 15
Subtract 45 from 48 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 9

Step 4:
9 goes into 37 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 154
Subtract 36 from 37 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 9

Step 5:
9 goes into 17 1 times with a remainder of 8.
Write down 1 as next digit of of the result. 
Result so far: 1541
Subtract 9 from 17 to get 8.

The final result is 1541 with a remainder of 8.