10259 ÷ 6 = 1709 R5
We're going to perform division on 10259 with 6 as the divisor.

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 (0) of the dividend behind the 1 and repeat the process: 10 / 6

Step 2:
6 goes into 10 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 10 to get 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 6

Step 3:
6 goes into 42 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 17
Subtract 42 from 42 to get 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 6

Step 4:
6 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 170
Subtract 0 from 5 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 6

Step 5:
6 goes into 59 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 1709
Subtract 54 from 59 to get 5.

The final result is 1709 with a remainder of 5.