370586 ÷ 89 
We're looking to find how many times 89 goes into 370586.

Advancing to step 1:
The number 89 fits into 3 0 times, leaving a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Take the next digit (7) from the dividend and append it to 3, then repeat: 37 / 89

Advancing to step 2:
The number 89 fits into 37 0 times, leaving a remainder of 37.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 37 to get 37.
Take the next digit (0) from the dividend and append it to 37, then repeat: 370 / 89

Let's proceed to step 3:
When dividing 370 by 89, we get 4 with a remainder of 14.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
If we subtract 356 from 370, we get 14.
Append the next digit (5) from the dividend to 14 and continue with: 145 / 89

Step 4:
89 can be fit into 145 1 times, resulting in a remainder of 56.
Use 1 as the next digit of our solution. 
Result so far: 41.0
If we take 89 away from 145, we end up with 56.
Append the next digit (8) from the dividend to 56 and continue with: 568 / 89

Going ahead to step 5:
If we divide 568 by 89, we get 6 and a remainder of 34.
Write down 6 as next digit of the result. 
Result so far: 416.0
If we take 534 away from 568, we end up with 34.
Grab the next digit (6) from the dividend, add it to 34, then carry on: 346 / 89

Moving on to step 6:
89 can be fit into 346 3 times, resulting in a remainder of 79.
Use 3 as the next digit of our solution. 
Result so far: 4163.0
If we subtract 267 from 346, we get 79.
Since there are no more digits in the dividend, we add a zero to the remainder making it 790, and continue the process.

Moving on to step 7:
The number 89 fits into 790 8 times, leaving a remainder of 78.
Use 8 as the next digit of our solution. 
Result so far: 4163.8
The remainder is 78 after subtracting 712 from 790.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Step 8:
The number 89 fits into 780 8 times, leaving a remainder of 68.
The next digit of our result is 8. 
Result so far: 4163.88
Subtracting 712 from 780 leaves us with 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

After the division, we end up with 4163.88 and a remainder of 0.068.