306601 ÷ 37 
Let's see how many times 37 fits into 306601.

Step 1:
3 divided by 37 is 0 with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Grab the next digit (0) from the dividend, add it to 3, then carry on: 30 / 37

Step 2:
30 divided by 37 is 0 with a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 30 leaves us with 30.
Grab the next digit (6) from the dividend, add it to 30, then carry on: 306 / 37

Let's proceed to step 3:
37 goes into 306 8 times with a remainder of 10.
Write down 8 as next digit of the result. 
Result so far: 8.0
Deduct 296 from 306 and we're left with 10.
Take the next digit (6) from the dividend and append it to 10, then repeat: 106 / 37

Step 4:
The number 37 fits into 106 2 times, leaving a remainder of 32.
Write down 2 as next digit of the result. 
Result so far: 82.0
Deduct 74 from 106 and we're left with 32.
Bring next digit (0) of the dividend behind the 32 and repeat the process: 320 / 37

Let's proceed to step 5:
When dividing 320 by 37, we get 8 with a remainder of 24.
Write down 8 as next digit of the result. 
Result so far: 828.0
Deduct 296 from 320 and we're left with 24.
Include the next digit (1) from the dividend after 24, then repeat: 241 / 37

Step 6:
37 can be fit into 241 6 times, resulting in a remainder of 19.
Use 6 as the next digit of our solution. 
Result so far: 8286.0
If we take 222 away from 241, we end up with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

On to step 7:
37 can be fit into 190 5 times, resulting in a remainder of 5.
The next digit of our result is 5. 
Result so far: 8286.5
Subtracting 185 from 190 leaves us 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.

Let's proceed to step 8:
37 can be fit into 50 1 times, resulting in a remainder of 13.
Put 1 as the next digit of the answer. 
Result so far: 8286.51
Deduct 37 from 50 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.

Advancing to step 9:
37 goes into 130 3 times with a remainder of 19.
The number 3 becomes the next digit in our result. 
Result so far: 8286.513
Deduct 111 from 130 and we're left with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Moving on to step 10:
37 goes into 190 5 times with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 8286.5135
Deduct 185 from 190 and we're left 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 11:
50 divided by 37 is 1 with a remainder of 13.
The next digit of our result is 1. 
Result so far: 8286.51351
If we subtract 37 from 50, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Let's proceed to step 12:
37 can be fit into 130 3 times, resulting in a remainder of 19.
The number 3 becomes the next digit in our result. 
Result so far: 8286.513513
Deduct 111 from 130 and we're left with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

On to step 13:
When dividing 190 by 37, we get 5 with a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 8286.5135135
If we subtract 185 from 190, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 14:
37 goes into 50 1 times with a remainder of 13.
Record the quotient 1 as the next digit in the result. 
Result so far: 8286.51351351
Deduct 37 from 50 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.

The final result is 8286.51351351 with a remainder of 1.3e-08.