Question

Determine how many zero end the number 300!+6415*125^10.​

Answer 1

Answer:

I think 2-3 zero or something else

Answer 2

Answer:

Well, we know that to have a zero at the end then 1010 must be a factor, which means 55 and 22 must be factors. However, every other factor is even, so there are far more factors of 22 than 55 - As such, we have to count the number of factors divisible by 55. The number of factors divisible by 55 less than or equal to 125125 is 2525 (we just do 12551255), so the answer appears to be 2525, but then we remember that 25=5⋅525=5⋅5, so we must count double for each factor divisible by 2525, of which there are 55; accordingly, our new answer is 3030. BUT WAIT... 125=53125=53, so we have to count it too, giving us a final answer of 31