16738 ÷ 3 = 5579 R1
Alright, let's work through the division of 16738 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 (6) of the dividend behind the 1 and repeat the process: 16 / 3

Step 2:
3 goes into 16 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 15 from 16 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 3

Step 3:
3 goes into 17 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 55
Subtract 15 from 17 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 3

Step 4:
3 goes into 23 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 557
Subtract 21 from 23 to get 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 3

Step 5:
3 goes into 28 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 5579
Subtract 27 from 28 to get 1.

The final result is 5579 with a remainder of 1.