11741 ÷ 7 = 1677 R2
Alright, let's work through the division of 11741 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 (7) of the dividend behind the 4 and repeat the process: 47 / 7

Step 3:
7 goes into 47 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 42 from 47 to get 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 7

Step 4:
7 goes into 54 7 times with a remainder of 5.
Write down 7 as next digit of of the result. 
Result so far: 167
Subtract 49 from 54 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 7

Step 5:
7 goes into 51 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 1677
Subtract 49 from 51 to get 2.

The final result is 1677 with a remainder of 2.