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richs_ca
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 Posted: Sat May 03, 2008 11:33 am Post subject: Prime factors |
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For all integers p, <<p>> is the product of p’s distinct prime factors. What is the greatest common factor of <<24>> and <<54>>?
a. <<2>>
b. <<3>>
c. <<8>>
d. <<12>>
e <<14>>
How do I figure this out? |
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Stuart Kovinsky
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| Posted: Sat May 03, 2008 11:56 am Post subject: Re: Prime factors |
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| richs_ca wrote: | For all integers p, <<p>> is the product of p’s distinct prime factors. What is the greatest common factor of <<24>> and <<54>>?
a. <<2>>
b. <<3>>
c. <<8>>
d. <<12>>
e <<14>>
How do I figure this out? |
Break it down!
54 = 2 * 27 = 2*3*3*3
So, the distinct prime factors of 54 are 2 and 3, and <<54>> is 2*3 = 6
24 = 2*12 = 2*2*2*3
So, <<24>> is also 2*3 = 6
Therefore, the GCF of <<24>> and <<54>> is 6.
Now, the answers are also in <<x>> form, so we want to pick a choice that's made up of 2s and 3s.
a) no 3
b) no 2
c) no 3
d) only 2s and 3s! Winner!
e) no 3
choose (d).
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simplyjat
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| Posted: Sat May 03, 2008 11:57 am Post subject: |
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The answer is d. <<12>>
So you know the definition of <<p>>.
To find <<24>>, break 24 in prime factors. 24 = 2*2*2*3. 2 and 3 are the only distinct prime factors and there product is 6. So <<24>> = 6
Similarly for <<54>>, 54 = 2*3*3*3 and <<54>> = 6
LCM of 6 & 6 is 6. So if the answers were provided in simple integers the answer would be 6. But the answer is a multiple of 6 or should only contain 2 and 3 as the only prime factors.
Looking at the answers <<12>> is the only answer that matches the criteria.
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