6645 ÷ 4 = 1661 R1
Let's divide 6645 by 4.

Step 1:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 6 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 4

Step 2:
4 goes into 26 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 24 from 26 to get 2.
Bring next digit (4) of the dividend behind the 2 and repeat the process: 24 / 4

Step 3:
4 goes into 24 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 166
Subtract 24 from 24 to get 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 4

Step 4:
4 goes into 5 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1661
Subtract 4 from 5 to get 1.

The final result is 1661 with a remainder of 1.