What is the least positive integer n such that n! divides 80325?
Wouldn't it be 1? If you're looking for the least positive integer that when factorialed divides 80325, then I think 1 fits the bill.
I mean, 1! is still 1, and every number can be divided by 1. Also, 1 is positive, and the LEAST positive integer there is. It fits the criteria, but I can agree with you that it seems like a "too easy" answer to the problem. Maybe you could try it?
...wait this is a homework problem...
...homework problems aren't supposed to be put here or answered here.
... I thought this was like a for fun problem on a website or something...
no, this is not. It is a practice question. I have done a lot so my score is really high. There higher the harder
There isn't one. I tried brute force. I divided 80325 by every n! starting at 1! and continuing through 8!. None* of them worked. The only possible answer is 1 and you've already dismissed that, so I don't know what to tell you. Maybe you copied the question incorrectly.
*Actually, they all divided into 80325. The problem doesn't state that the quotient has to be an integer, but in problems like this it is implied.
Had you actually tried to solve this question instead of trying to get others to do your work, you would not assume "oh well it is probably a 2 digit number"
For your information, a "two digit number" factorial, the least being 10!, is in the millions.
An integer can have any number of digits, just so long as it's a whole number, i.e., no fractional component. If that's what you mean. If you're remarking why did I stop at 8! it was because dividing by 8! gives a quotient ~ 1.99 so there's no point in dividing by any larger numbers.
Take prime factorization of this number.
For instance, if you get, 2^49 x 3^39 x 5^10
2^1 x 3^1 x 2^2 x 5^1, etc etc.
You could use that.
This number's prime factorization is
3^3 × 5^2 × 7 × 17
Anythiing higher than 1! will require a 2, but there is no two, and you're blatantly denying "1",
Other than 1, I see no solution.
Well 1 is wrong!
My bad/..... I'm stuck on this too
Find the largest integer n for which 12^n evenly divides 20!.