95574 ÷ 6 = 15929 R0
Alright, let's work through the division of 95574 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 (5) of the dividend behind the 3 and repeat the process: 35 / 6

Step 2:
6 goes into 35 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 15
Subtract 30 from 35 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 6

Step 3:
6 goes into 55 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 159
Subtract 54 from 55 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 6

Step 4:
6 goes into 17 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 1592
Subtract 12 from 17 to get 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 6

Step 5:
6 goes into 54 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 15929
Subtract 54 from 54 to get 0.

The final result is 15929 with a remainder of 0.