3782 ÷ 3 = 1260 R2
Alright, let's work through the division of 3782 by 3 step by step.

Step 1:
3 goes into 3 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 3 from 3 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: 12
Subtract 6 from 7 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 3

Step 3:
3 goes into 18 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 126
Subtract 18 from 18 to get 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 3

Step 4:
3 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 1260
Subtract 0 from 2 to get 2.

The final result is 1260 with a remainder of 2.