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The greatest common factor of 16 and the positive integer n [#permalink]
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21 Dec 2008, 05:18
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The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210? A. 3 B. 14 C. 30 D. 42 E. 70 OPEN DISCUSSION OF THIS QUESTION IS HERE: thegreatestcommonfactorof16andthepositiveintegern109870.html
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Re: Greatest Common Factor [#permalink]
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21 Dec 2008, 12:24
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I would say 42.
16 = 2^4. 16 and n have GCF as 2^2. That means, n could have only 2 twos as the factor.
45 = 5*3^2. 45 and have GCF as 3. That means, n will not have 5 as factor and only one 3 as the factor.
210 = 2*3*5*7 and since n does not have 5 as factor and n has 2^2 and 3 as factors, n could as well have 7 as a factor. Hence, 2*3*7 would be the greatest common factor.



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Re: Greatest Common Factor [#permalink]
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21 Dec 2008, 12:35
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The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210? a) 3 b) 14 c) 30 d) 42 e) 70
N= 4X, N=3Y THUS N = 12A
210 = 5*2*3*7
N HAS NO FACTOR 5 , US 42 COULD BE



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Re: Greatest Common Factor [#permalink]
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21 Dec 2008, 22:41
krishan wrote: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210? a) 3 b) 14 c) 30 d) 42 e) 70 210 = 5*2*3*7 N = 4x * 3 y = 2^2*3xy 6 must be the minimum common factor between n and 210. Answer must be divisible by 6 only 30 and 42 left. Maximum value could be 42. If answer choice has 210 then will chose 210
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Re: Greatest Common Factor [#permalink]
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22 Dec 2008, 08:55
im confused.
i got up to the point where 6 = lowest common factor.
then i understand that the answer has to be divisible by 6, therefore 30 or 42. why not 30?



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Re: Greatest Common Factor [#permalink]
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22 Dec 2008, 11:53
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sidrah wrote: im confused.
i got up to the point where 6 = lowest common factor.
then i understand that the answer has to be divisible by 6, therefore 30 or 42. why not 30? "Which of the following could be the greatest common factor of n and 210?"Question is asking about greatest common factor.. obviously.. 42>30.. so 42 is the answer.
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Re: Greatest Common Factor [#permalink]
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22 Dec 2008, 14:02
30 cannot be an answer because N cannot be divisible by 5 because:
45 has factors of 5x3x3. If N had a factor of 5, then 45 and Ns greatest common factor would be 5, not 3



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Re: Greatest Common Factor [#permalink]
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22 Dec 2008, 18:01
yay i geddit! =) was confused because simply coz 42 is bigger than 30 does not make it the right answer ... that would be assuming both are factors of n and 210. thank u x2suresh and username309



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Re: Greatest Common Factor [#permalink]
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23 Dec 2008, 12:35
krishan wrote: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210? a) 3 b) 14 c) 30 d) 42 e) 70 agree with 42. 16 = 2x2x2x2 45 = 3x3x5 n = 4 x 3 x k, where k is an integer 210 = 2x3x5x7 gcf of 16 and n = 4 gcf of n and 45 = 3 gcf of n and 210 = 2x3x7 (5 and 4 cannot be factors of n because 210 has only 2 as factor and n doesnot have 5 as factor) = 42 Another good question!!!!!!
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Re: Greatest Common Factor [#permalink]
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23 Dec 2008, 22:31
Since u have to find the GCF between 210 and n, go by the answer options.
first consider 70 = 7*5*2 . none of this coincides with conditions given. i.e GCF 4 and 3 is not obtained if u take 7*5*2.
move on to next option 42=7*2*3*k take k=1; one condition is matched. take k=2; both the conditions are matched . So answer is multiple of 42.



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Re: Greatest Common Factor [#permalink]
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24 May 2011, 05:27
FOR ME: NUMBER PRIME FACTORING N CANT BE INCLUDED IN N 16 2^4 2^2*X 2 OR 2^2 45 3^3*5 3*N 3 OR 5
210 PRIME FACTORIZATION IS 2*5*3*7
2, 5,3 CANT BE AND ONLY 7 HENCE:
7*2^2*3



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Re: Greatest Common Factor [#permalink]
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01 Apr 2014, 13:35
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Re: The greatest common factor of 16 and the positive integer n [#permalink]
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01 Apr 2014, 16:01
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210? A. 3 B. 14 C. 30 D. 42 E. 70 The greatest common factor of 2^4=16 and n is 4 > n is a multiple of 2^2=4 but not the higher powers of 2, for example 2^3=8 or 2^4=16, because if it were then the greatest common factor of 16 and n would be more than 4; The greatest common factor of 3^2*5=45 and n is 3 > n is a multiple of 3 but not the higher powers of 3 and not 5, because if it were then the greatest common factor of 3^2*5=45 and n would be more than 3; So, n is a multiple of 2^2*3=12, not a multiple of higher powers of 2 or 3, and not a multiple of 5 (so n=12x where x could be any positive integer but 2, 3, or 5). Now, as 210=2*3*5*7 then the greatest common factor of n and 210 could be 6 or 6*7=42 (if 7 is a factor of n). Answer: D. OPEN DISCUSSION OF THIS QUESTION IS HERE: thegreatestcommonfactorof16andthepositiveintegern109870.html
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Re: The greatest common factor of 16 and the positive integer n [#permalink]
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19 Apr 2014, 08:26
Not a proper but a random approach: GCD(n,16) = 4 n2^4 n must at least be a multiple of 4 GCD(n,45) = 3 n5*3^2 n must have one '3' and shouldn't have 5 Applying above restrictions calculating Max GCD(n,210) n2*3*5*7 N has one 3 and one 4 so n= 3*2*2 n cannot have 5 but can have 7 so n=2*2*3*7 2*3*5*7 Max(GCD) = 42
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Re: The greatest common factor of 16 and the positive integer n
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