19370 ÷ 3 = 6456 R2
Alright, let's work through the division of 19370 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 (9) of the dividend behind the 1 and repeat the process: 19 / 3

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

Step 3:
3 goes into 13 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 64
Subtract 12 from 13 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 3

Step 4:
3 goes into 17 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 645
Subtract 15 from 17 to get 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 3

Step 5:
3 goes into 20 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 6456
Subtract 18 from 20 to get 2.

The final result is 6456 with a remainder of 2.