SOLUTION: What is the smallest number that has 8 distinct prime factors? choose the answer and explain the reason to choose your response 510510 270270 9699690 256

Question 494977: What is the smallest number that has 8 distinct prime factors?
choose the answer and explain the reason to choose your response
510510
270270
9699690
256
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
By definition a prime number has two important limits. First, it must be greater than 1. Second it must only be divisible by 1 or by itself.
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This problem tells you to find the smallest possible number that has 8 distinct prime numbers as factors. Since this problem limits you to 8 prime numbers as factors and since each of the prime numbers is distinct (no using a prime number more than once), to get the smallest possible product you are limited to using the first 8 prime numbers.
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Here are the first 8 prime numbers: 2, 3, 5, 7, 11, 13, 17, and 19. Notice that each of these numbers is greater than 1, and each can only be divided evenly by itself and by 1.
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Multiply those 8 numbers together (use a calculator) and you will get the answer of 9699690.
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You can check the numbers between those 8 to see if any of them are prime. Then "in between" numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, and 18. All of these numbers except 9 and 15 are divisible by 2 so they can't be prime. And both 9 and 15 are divisible by 3 so they can't be prime. This helps to ensure that we have correctly got the first 8 prime numbers because none of the numbers that we skipped over was a prime number.
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Hope this helps you to understand the problem.
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