Of numbers in factorials

Actually I am facing troubles in these maths.

In the expression 1000/77^x , Greg chose the number 11 as 7 is a lower prime number as well as it appears frequently.

But in the expression 517/24^x , why did Greg choose 2??(2^3 × 3) if the number is divided by 2 , there are 258s two , but if the number is divided by 3, then there are 172s three. Aren’t we limited by the number of 3?? As 2 is occurring more than 3?

It’s because we use up three 2s each time we divide by 24, but only one 3. So we would actually run out of 2s first right?

In the 77 example, there’s only one of each.

Three 2s that means 8, right? Actually I have divided the number by 8 but the answer turned out different. So if there are similar cases like 5^3 and 7 we will choose three 5s??

Because the “trick” only works for primes, which 8 isn’t

Yes, because that runs out first.

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Thanks a lot,