45420 ÷ 8 = 5677 R4
Alright, let's work through the division of 45420 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 (5) of the dividend behind the 4 and repeat the process: 45 / 8

Step 2:
8 goes into 45 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 40 from 45 to get 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 8

Step 3:
8 goes into 54 6 times with a remainder of 6.
Write down 6 as next digit of of the result. 
Result so far: 56
Subtract 48 from 54 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: 567
Subtract 56 from 62 to get 6.
Bring next digit (0) of the dividend behind the 6 and repeat the process: 60 / 8

Step 5:
8 goes into 60 7 times with a remainder of 4.
Write down 7 as next digit of of the result. 
Result so far: 5677
Subtract 56 from 60 to get 4.

The final result is 5677 with a remainder of 4.