9586577 ÷ 542 
We want to figure out the number of times 9586577 can be divided by 542.

Advancing to step 1:
542 can be fit into 9 0 times, resulting in a remainder of 9.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 9, we end up with 9.
Take the next digit (5) from the dividend and append it to 9, then repeat: 95 / 542

Advancing to step 2:
If we divide 95 by 542, we get 0 and a remainder of 95.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 95, we end up with 95.
Fetch the next digit (8) from the dividend, attach it to 95 and continue: 958 / 542

Moving on to step 3:
When dividing 958 by 542, we get 1 with a remainder of 416.
The next digit of our result is 1. 
Result so far: 1.0
The remainder is 416 after subtracting 542 from 958.
Append the next digit (6) from the dividend to 416 and continue with: 4166 / 542

Moving on to step 4:
542 can be fit into 4166 7 times, resulting in a remainder of 372.
The number 7 becomes the next digit in our result. 
Result so far: 17.0
If we subtract 3794 from 4166, we get 372.
Append the next digit (5) from the dividend to 372 and continue with: 3725 / 542

Going ahead to step 5:
542 can be fit into 3725 6 times, resulting in a remainder of 473.
Put 6 as the next digit of the answer. 
Result so far: 176.0
Subtract 3252 from 3725 to get 473.
Append the next digit (7) from the dividend to 473 and continue with: 4737 / 542

Advancing to step 6:
The number 542 fits into 4737 8 times, leaving a remainder of 401.
Use 8 as the next digit of our solution. 
Result so far: 1768.0
If we take 4336 away from 4737, we end up with 401.
Grab the next digit (7) from the dividend, add it to 401, then carry on: 4017 / 542

Let's proceed to step 7:
The number 542 fits into 4017 7 times, leaving a remainder of 223.
The next digit of our result is 7. 
Result so far: 17687.0
Subtracting 3794 from 4017 leaves us with 223.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2230, and continue the process.

Going ahead to step 8:
542 can be fit into 2230 4 times, resulting in a remainder of 62.
Put 4 as the next digit of the answer. 
Result so far: 17687.4
Subtract 2168 from 2230 to get 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 9:
542 goes into 620 1 times with a remainder of 78.
Record the quotient 1 as the next digit in the result. 
Result so far: 17687.41
Deduct 542 from 620 and we're left with 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Going ahead to step 10:
542 goes into 780 1 times with a remainder of 238.
Record the quotient 1 as the next digit in the result. 
Result so far: 17687.411
If we subtract 542 from 780, we get 238.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2380, and continue the process.

In conclusion, the division gives 17687.411 with a balance of 0.0238.