75581 ÷ 3 = 25193 R2
Alright, let's work through the division of 75581 by 3 step by step.

Step 1:
3 goes into 7 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 6 from 7 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 3

Step 2:
3 goes into 15 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 25
Subtract 15 from 15 to get 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 3

Step 3:
3 goes into 5 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 251
Subtract 3 from 5 to get 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 3

Step 4:
3 goes into 28 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 2519
Subtract 27 from 28 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 3

Step 5:
3 goes into 11 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 25193
Subtract 9 from 11 to get 2.

The final result is 25193 with a remainder of 2.