SOLUTION: HI! My question is: Can you find any numbers that are less than 300 and are divisible by four different prime numbers? If yes, generate all of them and explain how you know your li

Question 344030: HI! My question is: Can you find any numbers that are less than 300 and are divisible by four different prime numbers? If yes, generate all of them and explain how you know your list is complete. If no, explain why none exist.
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
HI! My question is: Can you find any numbers that are less than 300 and are divisible by four different prime numbers? If yes, generate all of them and explain how you know your list is complete. If no, explain why none exist.

list of prime numbers from 2 to 293 (between 0 and 50, 15 primes)
2 3 5 7 11 -------------------------------> 5 numbers
13 17 19 23 29 31 37 41 43 47 ------------> 10 numbers

minimum product 4 primes: 2 * 3 * 5 * 7 = 6 * 5 * 7 = 30 * 7 = 210
next product 4 primes: 3 * 5 * 7 * 11 = 15 * 7 * 11 = 105 * 11 = 1155, too big
2 * 5 * 7 * 11 = 770, too big
minimum product of two 2-digit primes = 11 * 13 = 143, times 2 that is 286, times 3 it would be 429

from what I can tell, there is only one number less than 300 that is product of 4 primes, and that is 210

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