75601 ÷ 6 = 12600 R1
Alright, let's work through the division of 75601 by 6 step by step.

Step 1:
6 goes into 7 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 7 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 6

Step 2:
6 goes into 15 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 12
Subtract 12 from 15 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 6

Step 3:
6 goes into 36 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 126
Subtract 36 from 36 to get 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 6

Step 4:
6 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 1260
Subtract 0 from 0 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 6

Step 5:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 12600
Subtract 0 from 1 to get 1.

The final result is 12600 with a remainder of 1.