93877 ÷ 6 = 15646 R1
Alright, let's work through the division of 93877 by 6 step by step.

Step 1:
6 goes into 9 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 9 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 6

Step 2:
6 goes into 33 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 15
Subtract 30 from 33 to get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 6

Step 3:
6 goes into 38 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 156
Subtract 36 from 38 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 6

Step 4:
6 goes into 27 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 1564
Subtract 24 from 27 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 6

Step 5:
6 goes into 37 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 15646
Subtract 36 from 37 to get 1.

The final result is 15646 with a remainder of 1.