67960 ÷ 3 = 22653 R1
Alright, let's work through the division of 67960 by 3 step by step.

Step 1:
3 goes into 6 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 6 from 6 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 3

Step 2:
3 goes into 7 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 22
Subtract 6 from 7 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 3

Step 3:
3 goes into 19 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 226
Subtract 18 from 19 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 3

Step 4:
3 goes into 16 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 2265
Subtract 15 from 16 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 3

Step 5:
3 goes into 10 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 22653
Subtract 9 from 10 to get 1.

The final result is 22653 with a remainder of 1.