Question 715870: The question is what is the product of the distinct prime factors of 54? So my question is what are prime factors and I need help with this problem. Please and thank you. :)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
A factor of a composite number is a number other than 1 or the composite itself that divides the composite evenly. A prime factor is a factor that is a prime number. A prime number is an integer that has no other factors than 1 and the number itself, i.e. 2, 3, 5, 7 ... and so on.
When you break a number down to its prime factors, sometimes some of those factors are repeated. What they are asking here is to perform the prime factorization of the number 54, that is to say find the complete set of prime numbers that when multiplied together equals 54. Then take one each of the different prime factors and find the product of those distinct prime factors.
Prime factorization process:
Count the number of times that the original number is EVENLY divisible by 2. That is the number of factors of 2 that are in the number. Then count the number of factors of 3. Then 5, and then 7 if necessary. You don't need to go past 7 because the next prime number, 11, squared, i.e. 121 is greater than the number you are trying to factor.
Here are some hints as to divisibility:
1) Only even numbers are divisible by 2.
2) If the sum of the digits is divisible by 3, then the number is divisible by 3, otherwise not.
3) If the number ends in 0 or 5, then the number is divisible by 5, otherwise not.
4) Divisiblity by 7 is best tested by trial and error.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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