13135 ÷ 7 = 1876 R3
Alright, let's work through the division of 13135 by 7 step by step.

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 (1) of the dividend behind the 6 and repeat the process: 61 / 7

Step 3:
7 goes into 61 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 18
Subtract 56 from 61 to get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 7

Step 4:
7 goes into 53 7 times with a remainder of 4.
Write down 7 as next digit of of the result. 
Result so far: 187
Subtract 49 from 53 to get 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 7

Step 5:
7 goes into 45 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 1876
Subtract 42 from 45 to get 3.

The final result is 1876 with a remainder of 3.