365971 ÷ 31 
We want to divide 365971 by 31.

Advancing to step 1:
When dividing 3 by 31, we get 0 with a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Grab the next digit (6) from the dividend, add it to 3, then carry on: 36 / 31

Step 2:
31 goes into 36 1 times with a remainder of 5.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtract 31 from 36 to get 5.
Include the next digit (5) from the dividend after 5, then repeat: 55 / 31

Advancing to step 3:
If we divide 55 by 31, we get 1 and a remainder of 24.
Put 1 as the next digit of the answer. 
Result so far: 11.0
If we subtract 31 from 55, we get 24.
Include the next digit (9) from the dividend after 24, then repeat: 249 / 31

Step 4:
31 can be fit into 249 8 times, resulting in a remainder of 1.
Record the quotient 8 as the next digit in the result. 
Result so far: 118.0
If we subtract 248 from 249, we get 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 31

Step 5:
When dividing 17 by 31, we get 0 with a remainder of 17.
Write down 0 as next digit of the result. 
Result so far: 1180.0
Subtract 0 from 17 to get 17.
Append the next digit (1) from the dividend to 17 and continue with: 171 / 31

On to step 6:
31 can be fit into 171 5 times, resulting in a remainder of 16.
Use 5 as the next digit of our solution. 
Result so far: 11805.0
If we take 155 away from 171, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 7:
31 goes into 160 5 times with a remainder of 5.
The next digit of our result is 5. 
Result so far: 11805.5
If we take 155 away from 160, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 8:
31 goes into 50 1 times with a remainder of 19.
Put 1 as the next digit of the answer. 
Result so far: 11805.51
Subtract 31 from 50 to get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Let's proceed to step 9:
The number 31 fits into 190 6 times, leaving a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 11805.516
Subtracting 186 from 190 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 10:
31 goes into 40 1 times with a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 11805.5161
Deduct 31 from 40 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 11:
31 can be fit into 90 2 times, resulting in a remainder of 28.
Write down 2 as next digit of the result. 
Result so far: 11805.51612
If we subtract 62 from 90, we get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Moving on to step 12:
280 divided by 31 is 9 with a remainder of 1.
The next digit of our result is 9. 
Result so far: 11805.516129
If we subtract 279 from 280, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 13:
31 can be fit into 10 0 times, resulting in a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 11805.516129
Deduct 0 from 10 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 14:
100 divided by 31 is 3 with a remainder of 7.
The next digit of our result is 3. 
Result so far: 11805.51612903
If we take 93 away from 100, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

The quotient of the division is 11805.51612903, and the remainder is 7e-09.