60782 ÷ 6 = 10130 R2
Alright, let's work through the division of 60782 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 (0) of the dividend behind the 0 and repeat the process: 0 / 6

Step 2:
6 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 0 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 6

Step 3:
6 goes into 7 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 101
Subtract 6 from 7 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 6

Step 4:
6 goes into 18 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 1013
Subtract 18 from 18 to get 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 6

Step 5:
6 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 10130
Subtract 0 from 2 to get 2.

The final result is 10130 with a remainder of 2.