19737 divided by 65 
We want to figure out the number of times 19737 can be divided by 65.

On to step 1:
65 goes into 1 0 times with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Grab the next digit (9) from the dividend, add it to 1, then carry on: 19 / 65

Step 2:
If we divide 19 by 65, we get 0 and a remainder of 19.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 19, we end up with 19.
Take the next digit (7) from the dividend and append it to 19, then repeat: 197 / 65

Going ahead to step 3:
197 divided by 65 is 3 with a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
The remainder is 2 after subtracting 195 from 197.
Include the next digit (3) from the dividend after 2, then repeat: 23 / 65

On to step 4:
The number 65 fits into 23 0 times, leaving a remainder of 23.
Write down 0 as next digit of the result. 
Result so far: 30.0
Subtract 0 from 23 to get 23.
Fetch the next digit (7) from the dividend, attach it to 23 and continue: 237 / 65

Advancing to step 5:
237 divided by 65 is 3 with a remainder of 42.
Put 3 as the next digit of the answer. 
Result so far: 303.0
The remainder is 42 after subtracting 195 from 237.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Let's proceed to step 6:
420 divided by 65 is 6 with a remainder of 30.
The next digit of our result is 6. 
Result so far: 303.6
Subtracting 390 from 420 leaves us with 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 7:
300 divided by 65 is 4 with a remainder of 40.
Put 4 as the next digit of the answer. 
Result so far: 303.64
Subtracting 260 from 300 leaves us 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.

Step 8:
If we divide 400 by 65, we get 6 and a remainder of 10.
The next digit of our result is 6. 
Result so far: 303.646
If we take 390 away from 400, we end up 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.

Going ahead to step 9:
When dividing 100 by 65, we get 1 with a remainder of 35.
Use 1 as the next digit of our solution. 
Result so far: 303.6461
If we take 65 away from 100, we end up 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.

Going ahead to step 10:
The number 65 fits into 350 5 times, leaving a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 303.64615
If we subtract 325 from 350, we 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.

Let's proceed to step 11:
250 divided by 65 is 3 with a remainder of 55.
Record the quotient 3 as the next digit in the result. 
Result so far: 303.646153
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.

Moving on to step 12:
When dividing 550 by 65, we get 8 with a remainder of 30.
The number 8 becomes the next digit in our result. 
Result so far: 303.6461538
Subtract 520 from 550 to 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.

Advancing to step 13:
300 divided by 65 is 4 with a remainder of 40.
Record the quotient 4 as the next digit in the result. 
Result so far: 303.64615384
The remainder is 40 after subtracting 260 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

After the division, we end up with 303.64615384 and a remainder of 4e-08.