44876 ÷ 8 = 5609 R4
Alright, let's work through the division of 44876 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 (8) of the dividend behind the 4 and repeat the process: 48 / 8

Step 3:
8 goes into 48 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 56
Subtract 48 from 48 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 8

Step 4:
8 goes into 7 0 times with a remainder of 7.
Write down 0 as next digit of of the result. 
Result so far: 560
Subtract 0 from 7 to get 7.
Bring next digit (6) of the dividend behind the 7 and repeat the process: 76 / 8

Step 5:
8 goes into 76 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 5609
Subtract 72 from 76 to get 4.

The final result is 5609 with a remainder of 4.