4) There are three positive integers less than 100. One is a prime number, one is a composite number, and one is neither a prime number nor a composite number. Find the maximum possible value of the product of these three numbers.
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Jawaban:
To find the maximum possible value of the product of three positive integers less than 100, where one is a prime number, one is a composite number, and one is neither a prime number nor a composite number, we need to identify the largest numbers in each category.
1. Neither prime nor composite: The number 1 is neither prime nor composite[1].
2. Prime number: There are 25 prime numbers less than 100, with the largest prime number being 97[2].
3. Composite number: There are 74 composite numbers between 1 and 100, with the largest composite number being 100[3].
Now, we can calculate the maximum possible value of the product of these three numbers:
1 x 97 x 100 = 9700
Therefore, the maximum possible value of the product of these three numbers is 9,700.