421407 ÷ 61 
Our goal is to divide 421407 by 61.

Step 1:
61 goes into 4 0 times with a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 61

Let's proceed to step 2:
When dividing 42 by 61, we get 0 with a remainder of 42.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 42, we get 42.
Bring next digit (1) of the dividend behind the 42 and repeat the process: 421 / 61

Going ahead to step 3:
When dividing 421 by 61, we get 6 with a remainder of 55.
Write down 6 as next digit of the result. 
Result so far: 6.0
If we take 366 away from 421, we end up with 55.
Bring next digit (4) of the dividend behind the 55 and repeat the process: 554 / 61

Step 4:
61 goes into 554 9 times with a remainder of 5.
Record the quotient 9 as the next digit in the result. 
Result so far: 69.0
Subtracting 549 from 554 leaves us with 5.
Include the next digit (0) from the dividend after 5, then repeat: 50 / 61

Step 5:
61 goes into 50 0 times with a remainder of 50.
Write down 0 as next digit of the result. 
Result so far: 690.0
If we take 0 away from 50, we end up with 50.
Bring next digit (7) of the dividend behind the 50 and repeat the process: 507 / 61

On to step 6:
507 divided by 61 is 8 with a remainder of 19.
Record the quotient 8 as the next digit in the result. 
Result so far: 6908.0
Subtract 488 from 507 to get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Moving on to step 7:
61 can be fit into 190 3 times, resulting in a remainder of 7.
Put 3 as the next digit of the answer. 
Result so far: 6908.3
The remainder is 7 after subtracting 183 from 190.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 8:
If we divide 70 by 61, we get 1 and a remainder of 9.
The number 1 becomes the next digit in our result. 
Result so far: 6908.31
The remainder is 9 after subtracting 61 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 9:
When dividing 90 by 61, we get 1 with a remainder of 29.
The next digit of our result is 1. 
Result so far: 6908.311
If we subtract 61 from 90, we get 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Our division results in 6908.311 with a remaining 0.0029.