18274 ÷ 3 = 6091 R1
Alright, let's work through the division of 18274 by 3 step by step.

Step 1:
3 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 3

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

Step 3:
3 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 60
Subtract 0 from 2 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 3

Step 4:
3 goes into 27 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 609
Subtract 27 from 27 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 3

Step 5:
3 goes into 4 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 6091
Subtract 3 from 4 to get 1.

The final result is 6091 with a remainder of 1.