16573 ÷ 6 = 2762 R1
Alright, let's work through the division of 16573 by 6 step by step.

Step 1:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 6

Step 2:
6 goes into 16 2 times with a remainder of 4.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 12 from 16 to get 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 6

Step 3:
6 goes into 45 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 27
Subtract 42 from 45 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 6

Step 4:
6 goes into 37 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 276
Subtract 36 from 37 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 6

Step 5:
6 goes into 13 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 2762
Subtract 12 from 13 to get 1.

The final result is 2762 with a remainder of 1.