in this question, the answer is solved for 517/ 24^x.
the closest multiple of 24 to 517 is 504. should we not solve for that instead?
Hiya there! So for your question, you are thinking 24 times by x, but we are doing 24^x. So we are dealing with an exponent. We need to find the largest x so that 24^x divides 517! and we do that by finding how many 24’s are in the factorial by doing the following below:
So typically for these type of problems, we want to prime factorize the denominator. So, for 24 the prime factorization is 2^3 and 3^1. Now, we run out of 2s more than we run out of 3s, therefore we are limited by 2s. So now we do 517!/2^x.
When you do that, you get these numbers, and you have to add them up to 514. The next step is to address the 3 that we disregarded earlier, but all we do with that is just take the 514 we solved for and divide by 3 to get 171. That is how many 24s are in 517!
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