37877 ÷ 9 = 4208 R5
Alright, let's work through the division of 37877 by 9 step by step.

Step 1:
9 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 9

Step 2:
9 goes into 37 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 36 from 37 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 9

Step 3:
9 goes into 18 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 42
Subtract 18 from 18 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 9

Step 4:
9 goes into 7 0 times with a remainder of 7.
Write down 0 as next digit of of the result. 
Result so far: 420
Subtract 0 from 7 to get 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 9

Step 5:
9 goes into 77 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 4208
Subtract 72 from 77 to get 5.

The final result is 4208 with a remainder of 5.