371878 ÷ 45 
We're looking to find how many times 45 goes into 371878.

Let's proceed to step 1:
The number 45 fits into 3 0 times, leaving a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 45

Going ahead to step 2:
The number 45 fits into 37 0 times, leaving a remainder of 37.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 37 and we're left with 37.
Take the next digit (1) from the dividend and append it to 37, then repeat: 371 / 45

Step 3:
If we divide 371 by 45, we get 8 and a remainder of 11.
Use 8 as the next digit of our solution. 
Result so far: 8.0
Deduct 360 from 371 and we're left with 11.
Append the next digit (8) from the dividend to 11 and continue with: 118 / 45

Going ahead to step 4:
The number 45 fits into 118 2 times, leaving a remainder of 28.
Put 2 as the next digit of the answer. 
Result so far: 82.0
Subtract 90 from 118 to get 28.
Fetch the next digit (7) from the dividend, attach it to 28 and continue: 287 / 45

Going ahead to step 5:
When dividing 287 by 45, we get 6 with a remainder of 17.
Use 6 as the next digit of our solution. 
Result so far: 826.0
Subtracting 270 from 287 leaves us with 17.
Include the next digit (8) from the dividend after 17, then repeat: 178 / 45

Advancing to step 6:
When dividing 178 by 45, we get 3 with a remainder of 43.
Write down 3 as next digit of the result. 
Result so far: 8263.0
If we subtract 135 from 178, we get 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Advancing to step 7:
If we divide 430 by 45, we get 9 and a remainder of 25.
Use 9 as the next digit of our solution. 
Result so far: 8263.9
Deduct 405 from 430 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 8:
45 goes into 250 5 times with a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 8263.95
Deduct 225 from 250 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Going ahead to step 9:
45 goes into 250 5 times with a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 8263.955
The remainder is 25 after subtracting 225 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

In conclusion, the division gives 8263.955 with a balance of 0.0025.