21741 ÷ 7 = 3105 R6
Alright, let's work through the division of 21741 by 7 step by step.

Step 1:
7 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 2 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 7

Step 2:
7 goes into 21 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 21 from 21 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 7

Step 3:
7 goes into 7 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 31
Subtract 7 from 7 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 7

Step 4:
7 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 310
Subtract 0 from 4 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 7

Step 5:
7 goes into 41 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 3105
Subtract 35 from 41 to get 6.

The final result is 3105 with a remainder of 6.