44350 ÷ 7 = 6335 R5
Alright, let's work through the division of 44350 by 7 step by step.

Step 1:
7 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 4 to get 4.
Bring next digit (4) of the dividend behind the 4 and repeat the process: 44 / 7

Step 2:
7 goes into 44 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 42 from 44 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 7

Step 3:
7 goes into 23 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 63
Subtract 21 from 23 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 7

Step 4:
7 goes into 25 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 633
Subtract 21 from 25 to get 4.
Bring next digit (0) of the dividend behind the 4 and repeat the process: 40 / 7

Step 5:
7 goes into 40 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 6335
Subtract 35 from 40 to get 5.

The final result is 6335 with a remainder of 5.