Your method may have produced the (correct) number of 24 trailing zero's but it is not mathematically sound. Basically, you got luck by finding the correct number by employing a pathway that is not thoroughly logical.
I'll give a few examples :
It was logically thought thru.
I looked at the problem. Understood what was causing the zero's to be produced, calcuated how to work out which numbers produced the zeros and then described the method in simple terms.
