We look at the division of 641430 by 523 
We want to figure out the number of times 641430 can be divided by 523.

Going ahead to step 1:
The number 523 fits into 6 0 times, leaving a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 523

Advancing to step 2:
523 can be fit into 64 0 times, resulting in a remainder of 64.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 64 after subtracting 0 from 64.
Grab the next digit (1) from the dividend, add it to 64, then carry on: 641 / 523

Going ahead to step 3:
523 goes into 641 1 times with a remainder of 118.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 523 from 641, we get 118.
Take the next digit (4) from the dividend and append it to 118, then repeat: 1184 / 523

Let's proceed to step 4:
When dividing 1184 by 523, we get 2 with a remainder of 138.
Put 2 as the next digit of the answer. 
Result so far: 12.0
Subtract 1046 from 1184 to get 138.
Append the next digit (3) from the dividend to 138 and continue with: 1383 / 523

Advancing to step 5:
When dividing 1383 by 523, we get 2 with a remainder of 337.
Use 2 as the next digit of our solution. 
Result so far: 122.0
Subtract 1046 from 1383 to get 337.
Fetch the next digit (0) from the dividend, attach it to 337 and continue: 3370 / 523

Going ahead to step 6:
3370 divided by 523 is 6 with a remainder of 232.
Write down 6 as next digit of the result. 
Result so far: 1226.0
The remainder is 232 after subtracting 3138 from 3370.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2320, and continue the process.

On to step 7:
The number 523 fits into 2320 4 times, leaving a remainder of 228.
Put 4 as the next digit of the answer. 
Result so far: 1226.4
Subtract 2092 from 2320 to get 228.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2280, and continue the process.

Step 8:
2280 divided by 523 is 4 with a remainder of 188.
Use 4 as the next digit of our solution. 
Result so far: 1226.44
The remainder is 188 after subtracting 2092 from 2280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1880, and continue the process.

Our division results in 1226.44 with a remaining 0.188.