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What is the greatest common factor of positive integers x an  [#permalink]

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8 00:00

Difficulty:   35% (medium)

Question Stats: 60% (00:51) correct 40% (00:53) wrong based on 381 sessions

### HideShow timer Statistics What is the greatest common factor of positive integers x and y?

(1) x and y share only one common factor.
(2) x and y are unique prime numbers.

Considering statement 1 : If X = 6 and Y = 9 then X = 2*3 and Y = 3 *3 and the GCF is 3 which is the common factor shared by both X and Y and of X = 4 and Y = 12 then X = 2^2 and Y = 2^2 * 3. Therefore the GCF is 4. Therefore this statement should be insufficient.

Considering statement 2 : If X = 2 and Y = 3, the GCF is 1 as this is the common factor shared by both.

Hence, I went for B, which is not the case.

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Originally posted by enigma123 on 31 Dec 2013, 02:41.
Last edited by Bunuel on 31 Dec 2013, 03:53, edited 3 times in total.
Renamed the topic and edited the question.
Math Expert V
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Re: What is the greatest common factor of positive integers x an  [#permalink]

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2
2
enigma123 wrote:
What is the greatest common factor of positive integers x and y?

(1) x and y share only one common factor.
(2) x and y are unique prime numbers.

Considering statement 1 : If X = 6 and Y = 9 then X = 2*3 and Y = 3 *3 and the GCF is 3 which is the common factor shared by both X and Y and of X = 4 and Y = 12 then X = 2^2 and Y = 2^2 * 3. Therefore the GCF is 4. Therefore this statement should be insufficient.

Considering statement 2 : If X = 2 and Y = 3, the GCF is 1 as this is the common factor shared by both.

Hence, I went for B, which is not the case.

What is the greatest common factor of positive integers x and y?

(1) x and y share only one common factor --> every integer has 1 as a factor, thus since x and y share only one common factor it must be 1. Sufficient.

(2) x and y are unique prime numbers. Two different primes can have only 1 as common factor. Sufficient.

Hope it's clear.
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Re: What is the greatest common factor of positive integers x an  [#permalink]

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Let's start with (2). A prime number is only divisible by 1 and itself. Hence the factors of a prime number are only 1 and itself. Now if you have two DIFFERENT unique prime numbers, the factor is 1.

Statement (1). At first I started as you, thought about types of numbers sharing common divisors/factors. Then I remembered that every number is also divisible by 1 and itself. Hence, the numbers mustn't share another factor than one. Hence the GCD would again be 1. Thus D is the correct answer.
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Re: What is the greatest common factor of positive integers x an  [#permalink]

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Good question. Stmt 1 points that the common factor is 1 hence (1) is sufficient. Stmt 2 is also sufficient since two primes have 1 as the only common factor. D is the answer.
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Re: What is the greatest common factor of positive integers x an  [#permalink]

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Bunuel wrote:
enigma123 wrote:
What is the greatest common factor of positive integers x and y?

(1) x and y share only one common factor.
(2) x and y are unique prime numbers.

Considering statement 1 : If X = 6 and Y = 9 then X = 2*3 and Y = 3 *3 and the GCF is 3 which is the common factor shared by both X and Y and of X = 4 and Y = 12 then X = 2^2 and Y = 2^2 * 3. Therefore the GCF is 4. Therefore this statement should be insufficient.

Considering statement 2 : If X = 2 and Y = 3, the GCF is 1 as this is the common factor shared by both.

Hence, I went for B, which is not the case.

What is the greatest common factor of positive integers x and y?

(1) x and y share only one common factor --> every integer has 1 as a factor, thus since x and y share only one common factor it must be 1. Sufficient.

(2) x and y are unique prime numbers. Two different primes can have only 1 as common factor. Sufficient.

Hope it's clear.

(BUT) cant the two integers that is x and y be same??
thats y it should be C and not D
Math Expert V
Joined: 02 Sep 2009
Posts: 56260
Re: What is the greatest common factor of positive integers x an  [#permalink]

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Bunuel wrote:
enigma123 wrote:
What is the greatest common factor of positive integers x and y?

(1) x and y share only one common factor.
(2) x and y are unique prime numbers.

Considering statement 1 : If X = 6 and Y = 9 then X = 2*3 and Y = 3 *3 and the GCF is 3 which is the common factor shared by both X and Y and of X = 4 and Y = 12 then X = 2^2 and Y = 2^2 * 3. Therefore the GCF is 4. Therefore this statement should be insufficient.

Considering statement 2 : If X = 2 and Y = 3, the GCF is 1 as this is the common factor shared by both.

Hence, I went for B, which is not the case.

What is the greatest common factor of positive integers x and y?

(1) x and y share only one common factor --> every integer has 1 as a factor, thus since x and y share only one common factor it must be 1. Sufficient.

(2) x and y are unique prime numbers. Two different primes can have only 1 as common factor. Sufficient.

Hope it's clear.

(BUT) cant the two integers that is x and y be same??
thats y it should be C and not D

For (2) we are given that x and y are distinct: x and y are unique prime numbers.

As for (1): if x and y are the same number, say 3, then they would share all their factors 1 and 3, not just one.

The OA is correct.
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Re: What is the greatest common factor of positive integers x an  [#permalink]

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enigma123 wrote:
What is the greatest common factor of positive integers x and y?

(1) x and y share only one common factor.
(2) x and y are unique prime numbers.

Considering statement 1 : If X = 6 and Y = 9 then X = 2*3 and Y = 3 *3 and the GCF is 3 which is the common factor shared by both X and Y and of X = 4 and Y = 12 then X = 2^2 and Y = 2^2 * 3. Therefore the GCF is 4. Therefore this statement should be insufficient.

Considering statement 2 : If X = 2 and Y = 3, the GCF is 1 as this is the common factor shared by both.

Hence, I went for B, which is not the case.

1. one is the factor for all the values. since both has only one common factor then it should be one. hence suff.

2. two rpime number shares only one as a common factor. hence suff.

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Re: What is the greatest common factor of positive integers x an  [#permalink]

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we are not asked to find X and Y, just GCF

St1. Share only one factor means that X and Y are coprime. No matter what number they are (5,6 or 2,3) GCF=1.Suff

St2. X and Y unique primes means again that hey are coprime, so GCF=1.Suff

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Re: What is the greatest common factor of positive integers x an  [#permalink]

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_________________ Re: What is the greatest common factor of positive integers x an   [#permalink] 12 Jul 2018, 22:26
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