13877 ÷ 7 = 1982 R3
We're going to perform division on 13877 with 7 as the divisor.

Step 1:
7 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 / 7

Step 2:
7 goes into 13 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 13 to get 6.
Bring next digit (8) of the dividend behind the 6 and repeat the process: 68 / 7

Step 3:
7 goes into 68 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 19
Subtract 63 from 68 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 7

Step 4:
7 goes into 57 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 198
Subtract 56 from 57 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 7

Step 5:
7 goes into 17 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 1982
Subtract 14 from 17 to get 3.

The final result is 1982 with a remainder of 3.