1739 ÷ 6 = 289 R5
Alright, let's work through the division of 1739 by 6 step by step.

Step 1:
6 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 (7) of the dividend behind the 1 and repeat the process: 17 / 6

Step 2:
6 goes into 17 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 12 from 17 to get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 6

Step 3:
6 goes into 53 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 28
Subtract 48 from 53 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 6

Step 4:
6 goes into 59 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 289
Subtract 54 from 59 to get 5.

The final result is 289 with a remainder of 5.