4444 ÷ 4 = 1111 R0
No problem, we've got 4444 and 4 for the division.

Step 1:
4 goes into 4 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 4 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 4

Step 2:
4 goes into 4 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 4 from 4 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 4

Step 3:
4 goes into 4 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 111
Subtract 4 from 4 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 4

Step 4:
4 goes into 4 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1111
Subtract 4 from 4 to get 0.

The final result is 1111 with a remainder of 0.