11377 ÷ 7 = 1625 R2
Alright, let's work through the division of 11377 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 (1) of the dividend behind the 1 and repeat the process: 11 / 7

Step 2:
7 goes into 11 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 11 to get 4.
Bring next digit (3) of the dividend behind the 4 and repeat the process: 43 / 7

Step 3:
7 goes into 43 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 42 from 43 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 7

Step 4:
7 goes into 17 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 162
Subtract 14 from 17 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 7

Step 5:
7 goes into 37 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 1625
Subtract 35 from 37 to get 2.

The final result is 1625 with a remainder of 2.