75873 ÷ 6 = 12645 R3
Alright, let's work through the division of 75873 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 (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: 126
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: 1264
Subtract 24 from 27 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 6

Step 5:
6 goes into 33 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 12645
Subtract 30 from 33 to get 3.

The final result is 12645 with a remainder of 3.