We look at the division of 35970 by 60 
We're looking to find how many times 60 goes into 35970.

Advancing to step 1:
If we divide 3 by 60, we get 0 and 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.
Grab the next digit (5) from the dividend, add it to 3, then carry on: 35 / 60

Advancing to step 2:
The number 60 fits into 35 0 times, leaving a remainder of 35.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 35 leaves us with 35.
Take the next digit (9) from the dividend and append it to 35, then repeat: 359 / 60

Advancing to step 3:
When dividing 359 by 60, we get 5 with a remainder of 59.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Deduct 300 from 359 and we're left with 59.
Take the next digit (7) from the dividend and append it to 59, then repeat: 597 / 60

Step 4:
When dividing 597 by 60, we get 9 with a remainder of 57.
The number 9 becomes the next digit in our result. 
Result so far: 59.0
If we take 540 away from 597, we end up with 57.
Take the next digit (0) from the dividend and append it to 57, then repeat: 570 / 60

Step 5:
If we divide 570 by 60, we get 9 and a remainder of 30.
Put 9 as the next digit of the answer. 
Result so far: 599.0
The remainder is 30 after subtracting 540 from 570.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 6:
If we divide 300 by 60, we get 5 and a remainder of 0.
Put 5 as the next digit of the answer. 
Result so far: 599.5
Subtract 300 from 300 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.

Let's proceed to step 7:
60 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 599.5
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 60 is 0 with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 599.5
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Our division results in 599.5 with a remaining 0.0.