421514 ÷ 77 
Let's see how many times 77 fits into 421514.

Going ahead to step 1:
The number 77 fits into 4 0 times, leaving a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Fetch the next digit (2) from the dividend, attach it to 4 and continue: 42 / 77

On to step 2:
77 goes into 42 0 times with a remainder of 42.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 42 after subtracting 0 from 42.
Bring next digit (1) of the dividend behind the 42 and repeat the process: 421 / 77

Moving on to step 3:
421 divided by 77 is 5 with a remainder of 36.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we take 385 away from 421, we end up with 36.
Take the next digit (5) from the dividend and append it to 36, then repeat: 365 / 77

Moving on to step 4:
77 can be fit into 365 4 times, resulting in a remainder of 57.
Put 4 as the next digit of the answer. 
Result so far: 54.0
Subtracting 308 from 365 leaves us with 57.
Grab the next digit (1) from the dividend, add it to 57, then carry on: 571 / 77

Moving on to step 5:
When dividing 571 by 77, we get 7 with a remainder of 32.
Write down 7 as next digit of the result. 
Result so far: 547.0
If we take 539 away from 571, we end up with 32.
Take the next digit (4) from the dividend and append it to 32, then repeat: 324 / 77

On to step 6:
If we divide 324 by 77, we get 4 and a remainder of 16.
Record the quotient 4 as the next digit in the result. 
Result so far: 5474.0
Subtracting 308 from 324 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

On to step 7:
77 goes into 160 2 times with a remainder of 6.
The number 2 becomes the next digit in our result. 
Result so far: 5474.2
Subtracting 154 from 160 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 8:
If we divide 60 by 77, we get 0 and a remainder of 60.
The number 0 becomes the next digit in our result. 
Result so far: 5474.2
Subtracting 0 from 60 leaves us with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Let's proceed to step 9:
The number 77 fits into 600 7 times, leaving a remainder of 61.
Use 7 as the next digit of our solution. 
Result so far: 5474.207
If we subtract 539 from 600, we get 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Advancing to step 10:
The number 77 fits into 610 7 times, leaving a remainder of 71.
The number 7 becomes the next digit in our result. 
Result so far: 5474.2077
The remainder is 71 after subtracting 539 from 610.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

In conclusion, the division gives 5474.2077 with a balance of 0.00071.