70579 ÷ 9 = 7842 R1
Alright, let's work through the division of 70579 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 (0) of the dividend behind the 7 and repeat the process: 70 / 9

Step 2:
9 goes into 70 7 times with a remainder of 7.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 63 from 70 to get 7.
Bring next digit (5) of the dividend behind the 7 and repeat the process: 75 / 9

Step 3:
9 goes into 75 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 78
Subtract 72 from 75 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 9

Step 4:
9 goes into 37 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 784
Subtract 36 from 37 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 9

Step 5:
9 goes into 19 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 7842
Subtract 18 from 19 to get 1.

The final result is 7842 with a remainder of 1.