We're dividing 432617 by 31 
We want to figure out the number of times 432617 can be divided by 31.

Step 1:
If we divide 4 by 31, we get 0 and a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Append the next digit (3) from the dividend to 4 and continue with: 43 / 31

Moving on to step 2:
43 divided by 31 is 1 with a remainder of 12.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 31 from 43 to get 12.
Bring next digit (2) of the dividend behind the 12 and repeat the process: 122 / 31

Step 3:
31 goes into 122 3 times with a remainder of 29.
Put 3 as the next digit of the answer. 
Result so far: 13.0
Subtracting 93 from 122 leaves us with 29.
Take the next digit (6) from the dividend and append it to 29, then repeat: 296 / 31

Advancing to step 4:
31 can be fit into 296 9 times, resulting in a remainder of 17.
Write down 9 as next digit of the result. 
Result so far: 139.0
The remainder is 17 after subtracting 279 from 296.
Take the next digit (1) from the dividend and append it to 17, then repeat: 171 / 31

Step 5:
31 goes into 171 5 times with a remainder of 16.
Put 5 as the next digit of the answer. 
Result so far: 1395.0
Deduct 155 from 171 and we're left with 16.
Append the next digit (7) from the dividend to 16 and continue with: 167 / 31

Going ahead to step 6:
31 can be fit into 167 5 times, resulting in a remainder of 12.
The next digit of our result is 5. 
Result so far: 13955.0
Subtracting 155 from 167 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 7:
31 can be fit into 120 3 times, resulting in a remainder of 27.
Put 3 as the next digit of the answer. 
Result so far: 13955.3
If we take 93 away from 120, we end up 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.

Going ahead to step 8:
31 goes into 270 8 times with a remainder of 22.
The next digit of our result is 8. 
Result so far: 13955.38
If we subtract 248 from 270, we get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Advancing to step 9:
220 divided by 31 is 7 with a remainder of 3.
The number 7 becomes the next digit in our result. 
Result so far: 13955.387
Subtract 217 from 220 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 10:
30 divided by 31 is 0 with a remainder of 30.
The next digit of our result is 0. 
Result so far: 13955.387
If we take 0 away from 30, we end up 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.

Going ahead to step 11:
31 goes into 300 9 times with a remainder of 21.
The number 9 becomes the next digit in our result. 
Result so far: 13955.38709
Deduct 279 from 300 and we're left with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Advancing to step 12:
210 divided by 31 is 6 with a remainder of 24.
The number 6 becomes the next digit in our result. 
Result so far: 13955.387096
Deduct 186 from 210 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 13:
The number 31 fits into 240 7 times, leaving a remainder of 23.
Write down 7 as next digit of the result. 
Result so far: 13955.3870967
Subtracting 217 from 240 leaves us with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Moving on to step 14:
31 can be fit into 230 7 times, resulting in a remainder of 13.
The number 7 becomes the next digit in our result. 
Result so far: 13955.38709677
Deduct 217 from 230 and we're left with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Our division results in 13955.38709677 with a remaining 1.3e-08.