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11 Dec 2011, 06:23
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How do I know when prime factors are redundant?
Example: To find out whether x is divisible by 120, it's given that x is divisible by 12 and by 30.
We need three 2's, one 3 and one 5 for x to be divisible by 120, since x is divisible by 12, it's divisible by two 2's and a 3 and since x is divisible by 30, it's given that it has a 2, 5 and 3 in it's prime factorization. However, one of the 2's could be redundant. How do I know whether it's redundant or not? Is the fact that both 12 and 30 are multiples of 2 sufficient for one 2 to be redundant? Is there a general rule?
Example: To find out whether x is divisible by 120, it's given that x is divisible by 12 and by 30.
We need three 2's, one 3 and one 5 for x to be divisible by 120, since x is divisible by 12, it's divisible by two 2's and a 3 and since x is divisible by 30, it's given that it has a 2, 5 and 3 in it's prime factorization. However, one of the 2's could be redundant. How do I know whether it's redundant or not? Is the fact that both 12 and 30 are multiples of 2 sufficient for one 2 to be redundant? Is there a general rule?
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11 Dec 2011, 22:09
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You are basically right that you need all the factors - having two 2's in 12 and one 2 in 30 is not enough. You would need a factor with three 2's.
What's the source of you example?
In this case x could be 60, which is divisible by 12 and 30 but not by 120. We run into this problem because we do not have enough 2's (as you correctly noticed.)
I hope that helps!
What's the source of you example?
Quote:
In this case x could be 60, which is divisible by 12 and 30 but not by 120. We run into this problem because we do not have enough 2's (as you correctly noticed.)
I hope that helps!
12 Dec 2011, 12:46
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The redundancy is the "3", right? Therefore the answer is 360 because it includes all of the primes for 12, 30, and 120.
Please elaborate..
