7363 ÷ 7 = 1051 R6
Alright, let's work through the division of 7363 by 7 step by step.

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

Step 2:
7 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 3 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 7

Step 3:
7 goes into 36 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 105
Subtract 35 from 36 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 7

Step 4:
7 goes into 13 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 1051
Subtract 7 from 13 to get 6.

The final result is 1051 with a remainder of 6.