13877 ÷ 8 = 1734 R5
Let's divide 13877 by 8.

Step 1:
8 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 / 8

Step 2:
8 goes into 13 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 8 from 13 to get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 8

Step 3:
8 goes into 58 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 17
Subtract 56 from 58 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 8

Step 4:
8 goes into 27 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 173
Subtract 24 from 27 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 8

Step 5:
8 goes into 37 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 1734
Subtract 32 from 37 to get 5.

The final result is 1734 with a remainder of 5.