We're dividing 15614 by 65 
We want to figure out the number of times 15614 can be divided by 65.

Advancing to step 1:
When dividing 1 by 65, we get 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Grab the next digit (5) from the dividend, add it to 1, then carry on: 15 / 65

Step 2:
When dividing 15 by 65, we get 0 with a remainder of 15.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 15 and we're left with 15.
Fetch the next digit (6) from the dividend, attach it to 15 and continue: 156 / 65

On to step 3:
The number 65 fits into 156 2 times, leaving a remainder of 26.
Put 2 as the next digit of the answer. 
Result so far: 2.0
If we subtract 130 from 156, we get 26.
Grab the next digit (1) from the dividend, add it to 26, then carry on: 261 / 65

Let's proceed to step 4:
65 goes into 261 4 times with a remainder of 1.
Write down 4 as next digit of the result. 
Result so far: 24.0
If we subtract 260 from 261, we get 1.
Include the next digit (4) from the dividend after 1, then repeat: 14 / 65

Moving on to step 5:
When dividing 14 by 65, we get 0 with a remainder of 14.
Record the quotient 0 as the next digit in the result. 
Result so far: 240.0
If we subtract 0 from 14, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Going ahead to step 6:
If we divide 140 by 65, we get 2 and a remainder of 10.
Use 2 as the next digit of our solution. 
Result so far: 240.2
The remainder is 10 after subtracting 130 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 7:
The number 65 fits into 100 1 times, leaving a remainder of 35.
Use 1 as the next digit of our solution. 
Result so far: 240.21
Subtracting 65 from 100 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Step 8:
If we divide 350 by 65, we get 5 and a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 240.215
Subtracting 325 from 350 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 9:
The number 65 fits into 250 3 times, leaving a remainder of 55.
Record the quotient 3 as the next digit in the result. 
Result so far: 240.2153
Deduct 195 from 250 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.

Step 10:
If we divide 550 by 65, we get 8 and a remainder of 30.
Put 8 as the next digit of the answer. 
Result so far: 240.21538
If we subtract 520 from 550, 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.

Going ahead to step 11:
300 divided by 65 is 4 with a remainder of 40.
Write down 4 as next digit of the result. 
Result so far: 240.215384
If we take 260 away from 300, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 12:
The number 65 fits into 400 6 times, leaving a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 240.2153846
Deduct 390 from 400 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 13:
65 goes into 100 1 times with a remainder of 35.
Put 1 as the next digit of the answer. 
Result so far: 240.21538461
Subtract 65 from 100 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Our division results in 240.21538461 with a remaining 3.5e-08.