We're dividing 105641 by 95 
We want to figure out the number of times 105641 can be divided by 95.

Advancing to step 1:
95 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 95

Step 2:
If we divide 10 by 95, we get 0 and a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Fetch the next digit (5) from the dividend, attach it to 10 and continue: 105 / 95

Advancing to step 3:
95 goes into 105 1 times with a remainder of 10.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 95 from 105 to get 10.
Append the next digit (6) from the dividend to 10 and continue with: 106 / 95

Step 4:
If we divide 106 by 95, we get 1 and a remainder of 11.
The next digit of our result is 1. 
Result so far: 11.0
Deduct 95 from 106 and we're left with 11.
Bring next digit (4) of the dividend behind the 11 and repeat the process: 114 / 95

On to step 5:
114 divided by 95 is 1 with a remainder of 19.
Put 1 as the next digit of the answer. 
Result so far: 111.0
The remainder is 19 after subtracting 95 from 114.
Take the next digit (1) from the dividend and append it to 19, then repeat: 191 / 95

Going ahead to step 6:
If we divide 191 by 95, we get 2 and a remainder of 1.
Record the quotient 2 as the next digit in the result. 
Result so far: 1112.0
Deduct 190 from 191 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 7:
95 can be fit into 10 0 times, resulting in a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 1112.0
If we subtract 0 from 10, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 8:
If we divide 100 by 95, we get 1 and a remainder of 5.
The next digit of our result is 1. 
Result so far: 1112.01
If we take 95 away from 100, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 9:
50 divided by 95 is 0 with a remainder of 50.
Write down 0 as next digit of the result. 
Result so far: 1112.01
Subtracting 0 from 50 leaves us with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Step 10:
95 can be fit into 500 5 times, resulting in a remainder of 25.
Put 5 as the next digit of the answer. 
Result so far: 1112.0105
Subtract 475 from 500 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 11:
The number 95 fits into 250 2 times, leaving a remainder of 60.
The next digit of our result is 2. 
Result so far: 1112.01052
If we take 190 away from 250, we end up 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.

Step 12:
95 can be fit into 600 6 times, resulting in a remainder of 30.
The number 6 becomes the next digit in our result. 
Result so far: 1112.010526
If we subtract 570 from 600, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 13:
When dividing 300 by 95, we get 3 with a remainder of 15.
Write down 3 as next digit of the result. 
Result so far: 1112.0105263
Deduct 285 from 300 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 14:
95 goes into 150 1 times with a remainder of 55.
Write down 1 as next digit of the result. 
Result so far: 1112.01052631
Deduct 95 from 150 and we're left with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

The quotient of the division is 1112.01052631, and the remainder is 5.5e-08.