We look at the division of 25638669 by 141 
We're looking to find how many times 141 goes into 25638669.

On to step 1:
When dividing 2 by 141, we get 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Include the next digit (5) from the dividend after 2, then repeat: 25 / 141

Going ahead to step 2:
25 divided by 141 is 0 with a remainder of 25.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 25, we get 25.
Grab the next digit (6) from the dividend, add it to 25, then carry on: 256 / 141

On to step 3:
141 can be fit into 256 1 times, resulting in a remainder of 115.
The next digit of our result is 1. 
Result so far: 1.0
Deduct 141 from 256 and we're left with 115.
Grab the next digit (3) from the dividend, add it to 115, then carry on: 1153 / 141

Let's proceed to step 4:
141 goes into 1153 8 times with a remainder of 25.
Use 8 as the next digit of our solution. 
Result so far: 18.0
Deduct 1128 from 1153 and we're left with 25.
Bring next digit (8) of the dividend behind the 25 and repeat the process: 258 / 141

Moving on to step 5:
The number 141 fits into 258 1 times, leaving a remainder of 117.
The number 1 becomes the next digit in our result. 
Result so far: 181.0
Deduct 141 from 258 and we're left with 117.
Include the next digit (6) from the dividend after 117, then repeat: 1176 / 141

Moving on to step 6:
The number 141 fits into 1176 8 times, leaving a remainder of 48.
The next digit of our result is 8. 
Result so far: 1818.0
If we take 1128 away from 1176, we end up with 48.
Fetch the next digit (6) from the dividend, attach it to 48 and continue: 486 / 141

Going ahead to step 7:
If we divide 486 by 141, we get 3 and a remainder of 63.
The number 3 becomes the next digit in our result. 
Result so far: 18183.0
Subtracting 423 from 486 leaves us with 63.
Fetch the next digit (9) from the dividend, attach it to 63 and continue: 639 / 141

Advancing to step 8:
141 goes into 639 4 times with a remainder of 75.
The next digit of our result is 4. 
Result so far: 181834.0
Subtracting 564 from 639 leaves us with 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Step 9:
The number 141 fits into 750 5 times, leaving a remainder of 45.
The next digit of our result is 5. 
Result so far: 181834.5
Subtracting 705 from 750 leaves us with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Step 10:
The number 141 fits into 450 3 times, leaving a remainder of 27.
The number 3 becomes the next digit in our result. 
Result so far: 181834.53
Subtracting 423 from 450 leaves us with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Step 11:
If we divide 270 by 141, we get 1 and a remainder of 129.
The next digit of our result is 1. 
Result so far: 181834.531
Subtract 141 from 270 to get 129.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1290, and continue the process.

On to step 12:
If we divide 1290 by 141, we get 9 and a remainder of 21.
Use 9 as the next digit of our solution. 
Result so far: 181834.5319
Subtract 1269 from 1290 to get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

On to step 13:
210 divided by 141 is 1 with a remainder of 69.
Use 1 as the next digit of our solution. 
Result so far: 181834.53191
Subtracting 141 from 210 leaves us with 69.
Since there are no more digits in the dividend, we add a zero to the remainder making it 690, and continue the process.

Going ahead to step 14:
690 divided by 141 is 4 with a remainder of 126.
Record the quotient 4 as the next digit in the result. 
Result so far: 181834.531914
Subtract 564 from 690 to get 126.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1260, and continue the process.

Step 15:
141 can be fit into 1260 8 times, resulting in a remainder of 132.
Write down 8 as next digit of the result. 
Result so far: 181834.5319148
If we subtract 1128 from 1260, we get 132.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1320, and continue the process.

On to step 16:
141 goes into 1320 9 times with a remainder of 51.
Write down 9 as next digit of the result. 
Result so far: 181834.53191489
Subtract 1269 from 1320 to 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.

The final result is 181834.53191489 with a remainder of 5.1e-08.