309374 ÷ 89 
We want to figure out the number of times 309374 can be divided by 89.

Advancing to step 1:
3 divided by 89 is 0 with a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Append the next digit (0) from the dividend to 3 and continue with: 30 / 89

Advancing to step 2:
When dividing 30 by 89, we get 0 with a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 30, we end up with 30.
Take the next digit (9) from the dividend and append it to 30, then repeat: 309 / 89

Going ahead to step 3:
89 goes into 309 3 times with a remainder of 42.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
If we take 267 away from 309, we end up with 42.
Fetch the next digit (3) from the dividend, attach it to 42 and continue: 423 / 89

Moving on to step 4:
The number 89 fits into 423 4 times, leaving a remainder of 67.
The next digit of our result is 4. 
Result so far: 34.0
The remainder is 67 after subtracting 356 from 423.
Include the next digit (7) from the dividend after 67, then repeat: 677 / 89

Advancing to step 5:
89 goes into 677 7 times with a remainder of 54.
Use 7 as the next digit of our solution. 
Result so far: 347.0
Deduct 623 from 677 and we're left with 54.
Take the next digit (4) from the dividend and append it to 54, then repeat: 544 / 89

Going ahead to step 6:
If we divide 544 by 89, we get 6 and a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 3476.0
Subtract 534 from 544 to get 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 7:
When dividing 100 by 89, we get 1 with a remainder of 11.
The next digit of our result is 1. 
Result so far: 3476.1
Subtracting 89 from 100 leaves us with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 8:
89 can be fit into 110 1 times, resulting in a remainder of 21.
Put 1 as the next digit of the answer. 
Result so far: 3476.11
Subtracting 89 from 110 leaves us 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.

The quotient of the division is 3476.11, and the remainder is 0.021.