10586 ÷ 9 = 1176 R2
We're going to perform division on 10586 with 9 as the divisor.

Step 1:
9 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 (0) of the dividend behind the 1 and repeat the process: 10 / 9

Step 2:
9 goes into 10 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 9 from 10 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 9

Step 3:
9 goes into 15 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 9 from 15 to get 6.
Bring next digit (8) of the dividend behind the 6 and repeat the process: 68 / 9

Step 4:
9 goes into 68 7 times with a remainder of 5.
Write down 7 as next digit of of the result. 
Result so far: 117
Subtract 63 from 68 to get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 9

Step 5:
9 goes into 56 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 1176
Subtract 54 from 56 to get 2.

The final result is 1176 with a remainder of 2.