105251 ÷ 37 
Our goal is to divide 105251 by 37.

On to step 1:
When dividing 1 by 37, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 37

Advancing to step 2:
The number 37 fits into 10 0 times, leaving a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 10, we end up with 10.
Fetch the next digit (5) from the dividend, attach it to 10 and continue: 105 / 37

Let's proceed to step 3:
The number 37 fits into 105 2 times, leaving a remainder of 31.
Write down 2 as next digit of the result. 
Result so far: 2.0
Subtracting 74 from 105 leaves us with 31.
Include the next digit (2) from the dividend after 31, then repeat: 312 / 37

Moving on to step 4:
When dividing 312 by 37, we get 8 with a remainder of 16.
Write down 8 as next digit of the result. 
Result so far: 28.0
The remainder is 16 after subtracting 296 from 312.
Include the next digit (5) from the dividend after 16, then repeat: 165 / 37

Step 5:
37 can be fit into 165 4 times, resulting in a remainder of 17.
Write down 4 as next digit of the result. 
Result so far: 284.0
The remainder is 17 after subtracting 148 from 165.
Take the next digit (1) from the dividend and append it to 17, then repeat: 171 / 37

On to step 6:
37 can be fit into 171 4 times, resulting in a remainder of 23.
Put 4 as the next digit of the answer. 
Result so far: 2844.0
If we subtract 148 from 171, we get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Let's proceed to step 7:
37 can be fit into 230 6 times, resulting in a remainder of 8.
Record the quotient 6 as the next digit in the result. 
Result so far: 2844.6
The remainder is 8 after subtracting 222 from 230.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 8:
37 goes into 80 2 times with a remainder of 6.
Record the quotient 2 as the next digit in the result. 
Result so far: 2844.62
If we subtract 74 from 80, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 9:
If we divide 60 by 37, we get 1 and a remainder of 23.
Put 1 as the next digit of the answer. 
Result so far: 2844.621
If we take 37 away from 60, we end up 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 10:
If we divide 230 by 37, we get 6 and a remainder of 8.
The next digit of our result is 6. 
Result so far: 2844.6216
Deduct 222 from 230 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 11:
When dividing 80 by 37, we get 2 with a remainder of 6.
Use 2 as the next digit of our solution. 
Result so far: 2844.62162
Subtract 74 from 80 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 12:
37 goes into 60 1 times with a remainder of 23.
The number 1 becomes the next digit in our result. 
Result so far: 2844.621621
If we take 37 away from 60, we end up 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.

Step 13:
When dividing 230 by 37, we get 6 with a remainder of 8.
Write down 6 as next digit of the result. 
Result so far: 2844.6216216
Deduct 222 from 230 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 14:
37 can be fit into 80 2 times, resulting in a remainder of 6.
Write down 2 as next digit of the result. 
Result so far: 2844.62162162
Subtracting 74 from 80 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

The quotient of the division is 2844.62162162, and the remainder is 6e-09.