Highest Possible Value for (Part 4)
What is the largest possible integer value of such that is also an integer?
The answer is 24.
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1 solution
Since 2 and 5 are the prime factors of 10, you need to find how many times 2 and 5 are factors of 100!. It's obvious 2 is a factor of more numbers than 5,so you need to count it for 5. 5 divides 20 numbers at least once(5,10,15, etc). Among those 20 there are 4 which has 5 as a factor twice: 25,50,75 and 100. Since 5^3 = 125, there's no need to look further, hence the answer is 24.