421427 ÷ 64 
Our goal is to divide 421427 by 64.

Moving on to step 1:
64 goes into 4 0 times with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Grab the next digit (2) from the dividend, add it to 4, then carry on: 42 / 64

Advancing to step 2:
If we divide 42 by 64, we get 0 and a remainder of 42.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 42 and we're left with 42.
Fetch the next digit (1) from the dividend, attach it to 42 and continue: 421 / 64

Let's proceed to step 3:
The number 64 fits into 421 6 times, leaving a remainder of 37.
Put 6 as the next digit of the answer. 
Result so far: 6.0
If we take 384 away from 421, we end up with 37.
Fetch the next digit (4) from the dividend, attach it to 37 and continue: 374 / 64

Advancing to step 4:
64 goes into 374 5 times with a remainder of 54.
The next digit of our result is 5. 
Result so far: 65.0
Subtracting 320 from 374 leaves us with 54.
Fetch the next digit (2) from the dividend, attach it to 54 and continue: 542 / 64

Advancing to step 5:
The number 64 fits into 542 8 times, leaving a remainder of 30.
Use 8 as the next digit of our solution. 
Result so far: 658.0
The remainder is 30 after subtracting 512 from 542.
Fetch the next digit (7) from the dividend, attach it to 30 and continue: 307 / 64

Let's proceed to step 6:
64 goes into 307 4 times with a remainder of 51.
The number 4 becomes the next digit in our result. 
Result so far: 6584.0
If we subtract 256 from 307, we get 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Let's proceed to step 7:
64 can be fit into 510 7 times, resulting in a remainder of 62.
Record the quotient 7 as the next digit in the result. 
Result so far: 6584.7
Deduct 448 from 510 and we're left with 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Let's proceed to step 8:
When dividing 620 by 64, we get 9 with a remainder of 44.
Put 9 as the next digit of the answer. 
Result so far: 6584.79
Deduct 576 from 620 and we're left with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Advancing to step 9:
64 can be fit into 440 6 times, resulting in a remainder of 56.
The number 6 becomes the next digit in our result. 
Result so far: 6584.796
The remainder is 56 after subtracting 384 from 440.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

On to step 10:
When dividing 560 by 64, we get 8 with a remainder of 48.
Record the quotient 8 as the next digit in the result. 
Result so far: 6584.7968
Deduct 512 from 560 and we're left with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Advancing to step 11:
When dividing 480 by 64, we get 7 with a remainder of 32.
The number 7 becomes the next digit in our result. 
Result so far: 6584.79687
Subtract 448 from 480 to get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Let's proceed to step 12:
64 goes into 320 5 times with a remainder of 0.
The next digit of our result is 5. 
Result so far: 6584.796875
The remainder is 0 after subtracting 320 from 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 13:
When dividing 0 by 64, we get 0 with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 6584.796875
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 14:
If we divide 0 by 64, we get 0 and a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 6584.796875
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 6584.796875, and the remainder is 0.0.