41963 ÷ 7 = 5994 R5
Alright, let's work through the division of 41963 by 7 step by step.

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

Step 2:
7 goes into 41 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 35 from 41 to get 6.
Bring next digit (9) of the dividend behind the 6 and repeat the process: 69 / 7

Step 3:
7 goes into 69 9 times with a remainder of 6.
Write down 9 as next digit of of the result. 
Result so far: 59
Subtract 63 from 69 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 7

Step 4:
7 goes into 66 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 599
Subtract 63 from 66 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 7

Step 5:
7 goes into 33 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 5994
Subtract 28 from 33 to get 5.

The final result is 5994 with a remainder of 5.