51577 ÷ 6 = 8596 R1
We're going to perform division on 51577 with 6 as the divisor.

Step 1:
6 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 6

Step 2:
6 goes into 51 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 48 from 51 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 6

Step 3:
6 goes into 35 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 85
Subtract 30 from 35 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 6

Step 4:
6 goes into 57 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 859
Subtract 54 from 57 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: 8596
Subtract 36 from 37 to get 1.

The final result is 8596 with a remainder of 1.