78013 ÷ 9 = 8668 R1
Alright, let's work through the division of 78013 by 9 step by step.

Step 1:
9 goes into 7 0 times with a remainder of 7.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 7 to get 7.
Bring next digit (8) of the dividend behind the 7 and repeat the process: 78 / 9

Step 2:
9 goes into 78 8 times with a remainder of 6.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 72 from 78 to get 6.
Bring next digit (0) of the dividend behind the 6 and repeat the process: 60 / 9

Step 3:
9 goes into 60 6 times with a remainder of 6.
Write down 6 as next digit of of the result. 
Result so far: 86
Subtract 54 from 60 to get 6.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 9

Step 4:
9 goes into 61 6 times with a remainder of 7.
Write down 6 as next digit of of the result. 
Result so far: 866
Subtract 54 from 61 to get 7.
Bring next digit (3) of the dividend behind the 7 and repeat the process: 73 / 9

Step 5:
9 goes into 73 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 8668
Subtract 72 from 73 to get 1.

The final result is 8668 with a remainder of 1.