4375 ÷ 8 = 546 R7
Alright, let's work through the division of 4375 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 (3) of the dividend behind the 4 and repeat the process: 43 / 8

Step 2:
8 goes into 43 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 40 from 43 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 8

Step 3:
8 goes into 37 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 54
Subtract 32 from 37 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 8

Step 4:
8 goes into 55 6 times with a remainder of 7.
Write down 6 as next digit of of the result. 
Result so far: 546
Subtract 48 from 55 to get 7.

The final result is 546 with a remainder of 7.