6597 ÷ 5 = 1319 R2
Let's divide 6597 by 5.

Step 1:
5 goes into 6 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 5 from 6 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 5

Step 2:
5 goes into 15 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 15 from 15 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 5

Step 3:
5 goes into 9 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 131
Subtract 5 from 9 to get 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 5

Step 4:
5 goes into 47 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 1319
Subtract 45 from 47 to get 2.

The final result is 1319 with a remainder of 2.