62633 ÷ 6 = 10438 R5
Alright, let's work through the division of 62633 by 6 step by step.

Step 1:
6 goes into 6 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 6 to get 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 6

Step 2:
6 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 2 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 6

Step 3:
6 goes into 26 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 104
Subtract 24 from 26 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 6

Step 4:
6 goes into 23 3 times with a remainder of 5.
Write down 3 as next digit of of the result. 
Result so far: 1043
Subtract 18 from 23 to get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 6

Step 5:
6 goes into 53 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 10438
Subtract 48 from 53 to get 5.

The final result is 10438 with a remainder of 5.