587351 ÷ 45 
We're looking to find how many times 45 goes into 587351.

Advancing to step 1:
When dividing 5 by 45, we get 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 45

Advancing to step 2:
The number 45 fits into 58 1 times, leaving a remainder of 13.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtracting 45 from 58 leaves us with 13.
Grab the next digit (7) from the dividend, add it to 13, then carry on: 137 / 45

Advancing to step 3:
45 goes into 137 3 times with a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
Subtract 135 from 137 to get 2.
Take the next digit (3) from the dividend and append it to 2, then repeat: 23 / 45

Moving on to step 4:
23 divided by 45 is 0 with a remainder of 23.
Record the quotient 0 as the next digit in the result. 
Result so far: 130.0
The remainder is 23 after subtracting 0 from 23.
Take the next digit (5) from the dividend and append it to 23, then repeat: 235 / 45

Let's proceed to step 5:
45 can be fit into 235 5 times, resulting in a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 1305.0
Subtract 225 from 235 to get 10.
Bring next digit (1) of the dividend behind the 10 and repeat the process: 101 / 45

On to step 6:
45 goes into 101 2 times with a remainder of 11.
Write down 2 as next digit of the result. 
Result so far: 13052.0
Deduct 90 from 101 and we're left 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.

Step 7:
The number 45 fits into 110 2 times, leaving a remainder of 20.
Record the quotient 2 as the next digit in the result. 
Result so far: 13052.2
The remainder is 20 after subtracting 90 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 8:
45 can be fit into 200 4 times, resulting in a remainder of 20.
Use 4 as the next digit of our solution. 
Result so far: 13052.24
Subtract 180 from 200 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Going ahead to step 9:
If we divide 200 by 45, we get 4 and a remainder of 20.
Write down 4 as next digit of the result. 
Result so far: 13052.244
The remainder is 20 after subtracting 180 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The final outcome is 13052.244, with a leftover of 0.002.