63590 ÷ 6 = 10598 R2
Alright, let's work through the division of 63590 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 (3) of the dividend behind the 0 and repeat the process: 3 / 6

Step 2:
6 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 3 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 6

Step 3:
6 goes into 35 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 105
Subtract 30 from 35 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 6

Step 4:
6 goes into 59 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 1059
Subtract 54 from 59 to get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 6

Step 5:
6 goes into 50 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 10598
Subtract 48 from 50 to get 2.

The final result is 10598 with a remainder of 2.