61407 ÷ 6 = 10234 R3
Alright, let's work through the division of 61407 by 6 step by step.

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

Step 2:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 1 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 6

Step 3:
6 goes into 14 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 102
Subtract 12 from 14 to get 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 6

Step 4:
6 goes into 20 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 1023
Subtract 18 from 20 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 6

Step 5:
6 goes into 27 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 10234
Subtract 24 from 27 to get 3.

The final result is 10234 with a remainder of 3.