6644 ÷ 7 = 949 R1
Alright, let's work through the division of 6644 by 7 step by step.

Step 1:
7 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 6 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 7

Step 2:
7 goes into 66 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 9
Subtract 63 from 66 to get 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 7

Step 3:
7 goes into 34 4 times with a remainder of 6.
Write down 4 as next digit of of the result. 
Result so far: 94
Subtract 28 from 34 to get 6.
Bring next digit (4) of the dividend behind the 6 and repeat the process: 64 / 7

Step 4:
7 goes into 64 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 949
Subtract 63 from 64 to get 1.

The final result is 949 with a remainder of 1.