79001 ÷ 6 = 13166 R5
Alright, let's work through the division of 79001 by 6 step by step.

Step 1:
6 goes into 7 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 7 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 6

Step 2:
6 goes into 19 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 18 from 19 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 6

Step 3:
6 goes into 10 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 131
Subtract 6 from 10 to get 4.
Bring next digit (0) of the dividend behind the 4 and repeat the process: 40 / 6

Step 4:
6 goes into 40 6 times with a remainder of 4.
Write down 6 as next digit of of the result. 
Result so far: 1316
Subtract 36 from 40 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 6

Step 5:
6 goes into 41 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 13166
Subtract 36 from 41 to get 5.

The final result is 13166 with a remainder of 5.