13661 ÷ 89 
We're looking to find how many times 89 goes into 13661.

Let's proceed to step 1:
89 can be fit into 1 0 times, resulting in a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 89

Advancing to step 2:
89 goes into 13 0 times with a remainder of 13.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 13, we get 13.
Take the next digit (6) from the dividend and append it to 13, then repeat: 136 / 89

On to step 3:
If we divide 136 by 89, we get 1 and a remainder of 47.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 89 from 136 to get 47.
Bring next digit (6) of the dividend behind the 47 and repeat the process: 476 / 89

On to step 4:
89 goes into 476 5 times with a remainder of 31.
The next digit of our result is 5. 
Result so far: 15.0
Subtract 445 from 476 to get 31.
Include the next digit (1) from the dividend after 31, then repeat: 311 / 89

Let's proceed to step 5:
If we divide 311 by 89, we get 3 and a remainder of 44.
Put 3 as the next digit of the answer. 
Result so far: 153.0
The remainder is 44 after subtracting 267 from 311.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Step 6:
The number 89 fits into 440 4 times, leaving a remainder of 84.
Put 4 as the next digit of the answer. 
Result so far: 153.4
Deduct 356 from 440 and we're left with 84.
Since there are no more digits in the dividend, we add a zero to the remainder making it 840, and continue the process.

Moving on to step 7:
The number 89 fits into 840 9 times, leaving a remainder of 39.
Use 9 as the next digit of our solution. 
Result so far: 153.49
Subtract 801 from 840 to get 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

On to step 8:
When dividing 390 by 89, we get 4 with a remainder of 34.
Put 4 as the next digit of the answer. 
Result so far: 153.494
The remainder is 34 after subtracting 356 from 390.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 9:
89 can be fit into 340 3 times, resulting in a remainder of 73.
Put 3 as the next digit of the answer. 
Result so far: 153.4943
If we subtract 267 from 340, we get 73.
Since there are no more digits in the dividend, we add a zero to the remainder making it 730, and continue the process.

Advancing to step 10:
When dividing 730 by 89, we get 8 with a remainder of 18.
The next digit of our result is 8. 
Result so far: 153.49438
Subtracting 712 from 730 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Let's proceed to step 11:
The number 89 fits into 180 2 times, leaving a remainder of 2.
Use 2 as the next digit of our solution. 
Result so far: 153.494382
Subtracting 178 from 180 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 12:
89 can be fit into 20 0 times, resulting in a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 153.494382
If we take 0 away from 20, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 13:
200 divided by 89 is 2 with a remainder of 22.
Use 2 as the next digit of our solution. 
Result so far: 153.49438202
Subtracting 178 from 200 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

After the division, we end up with 153.49438202 and a remainder of 2.2e-08.