We're dividing 537876 by 9 
We want to figure out the number of times 537876 can be divided by 9.

Step 1:
When dividing 5 by 9, we get 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Fetch the next digit (3) from the dividend, attach it to 5 and continue: 53 / 9

Going ahead to step 2:
The number 9 fits into 53 5 times, leaving a remainder of 8.
Put 5 as the next digit of the answer. 
Result so far: 5.0
Subtracting 45 from 53 leaves us with 8.
Take the next digit (7) from the dividend and append it to 8, then repeat: 87 / 9

Advancing to step 3:
If we divide 87 by 9, we get 9 and a remainder of 6.
Put 9 as the next digit of the answer. 
Result so far: 59.0
If we take 81 away from 87, we end up with 6.
Take the next digit (8) from the dividend and append it to 6, then repeat: 68 / 9

Going ahead to step 4:
If we divide 68 by 9, we get 7 and a remainder of 5.
Record the quotient 7 as the next digit in the result. 
Result so far: 597.0
If we subtract 63 from 68, we get 5.
Take the next digit (7) from the dividend and append it to 5, then repeat: 57 / 9

Step 5:
9 goes into 57 6 times with a remainder of 3.
Record the quotient 6 as the next digit in the result. 
Result so far: 5976.0
Deduct 54 from 57 and we're left with 3.
Grab the next digit (6) from the dividend, add it to 3, then carry on: 36 / 9

Advancing to step 6:
9 goes into 36 4 times with a remainder of 0.
Put 4 as the next digit of the answer. 
Result so far: 59764.0
Subtract 36 from 36 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 7:
If we divide 0 by 9, we get 0 and a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 59764.0
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 8:
0 divided by 9 is 0 with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 59764.0
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

After the division, we end up with 59764.0 and a remainder of 0.0.