10097 ÷ 7 = 1442 R3
Alright, let's work through the division of 10097 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 (0) of the dividend behind the 1 and repeat the process: 10 / 7

Step 2:
7 goes into 10 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 10 to get 3.
Bring next digit (0) of the dividend behind the 3 and repeat the process: 30 / 7

Step 3:
7 goes into 30 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 14
Subtract 28 from 30 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 7

Step 4:
7 goes into 29 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 144
Subtract 28 from 29 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 7

Step 5:
7 goes into 17 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 1442
Subtract 14 from 17 to get 3.

The final result is 1442 with a remainder of 3.