44628 ÷ 8 = 5578 R4
Alright, let's work through the division of 44628 by 8 step by step.

Step 1:
8 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 / 8

Step 2:
8 goes into 44 5 times with a remainder of 4.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 40 from 44 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 8

Step 3:
8 goes into 46 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 55
Subtract 40 from 46 to get 6.
Bring next digit (2) of the dividend behind the 6 and repeat the process: 62 / 8

Step 4:
8 goes into 62 7 times with a remainder of 6.
Write down 7 as next digit of of the result. 
Result so far: 557
Subtract 56 from 62 to get 6.
Bring next digit (8) of the dividend behind the 6 and repeat the process: 68 / 8

Step 5:
8 goes into 68 8 times with a remainder of 4.
Write down 8 as next digit of of the result. 
Result so far: 5578
Subtract 64 from 68 to get 4.

The final result is 5578 with a remainder of 4.