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Which of the following could be the greatest common factor of positive

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Which of the following could be the greatest common factor of positive [#permalink]

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Which of the following could be the greatest common factor of positive integers a and b?

I. 1
II. a
III. a-b

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III
[Reveal] Spoiler: OA
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Re: Which of the following could be the greatest common factor of positive [#permalink]

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New post 01 Jun 2016, 09:09
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pepo wrote:
which of the following could be the greatest common factor of positive integers a and b?

I. 1
II. a
III. a-b

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III


It could be 1 if a and b are co-prime, for example, 1 and 2, 11 and 13...

It could be a itself if a is a factor of b, for example, 2 and 4, 5 and 15...

It could be a-b, for example, when a=b+1: a=2 and b=1, a=3 and b=2...

Answer: E.
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Re: Which of the following could be the greatest common factor of positive [#permalink]

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New post 28 Jan 2017, 07:47
Bunuel wrote:
pepo wrote:
which of the following could be the greatest common factor of positive integers a and b?

I. 1
II. a
III. a-b

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III


It could be 1 if a and b are co-prime, for example, 1 and 2, 11 and 13...

It could be a itself if a is a factor of b, for example, 2 and 4, 5 and 15...

It could be a-b, for example, when a=b+1: a=2 and b=1, a=3 and b=2...

Answer: E.



Since greatest is asked it should be a single number not 3 numbers.
Correct me if I'm wrong
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Re: Which of the following could be the greatest common factor of positive [#permalink]

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New post 28 Jan 2017, 07:50
Raahan wrote:
Bunuel wrote:
pepo wrote:
which of the following could be the greatest common factor of positive integers a and b?

I. 1
II. a
III. a-b

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III


It could be 1 if a and b are co-prime, for example, 1 and 2, 11 and 13...

It could be a itself if a is a factor of b, for example, 2 and 4, 5 and 15...

It could be a-b, for example, when a=b+1: a=2 and b=1, a=3 and b=2...

Answer: E.



Since greatest is asked it should be a single number not 3 numbers.
Correct me if I'm wrong


The question asks which of the following could be the greatest common factor (GCF) of positive integers a and b? All three (for different cases) could be the greatest common factors of a and b. So, the answer is E.
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Re: Which of the following could be the greatest common factor of positive [#permalink]

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New post 30 May 2017, 22:43
Bunuel

In the third case (a-b), a and b can also be 6 and 4?
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Re: Which of the following could be the greatest common factor of positive [#permalink]

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Re: Which of the following could be the greatest common factor of positive [#permalink]

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New post 31 May 2017, 16:45
The GCF of 4,10 is 2, which does not fall into any of the 3 categories right?
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Re: Which of the following could be the greatest common factor of positive [#permalink]

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New post 31 May 2017, 18:36
Hi,

I am confused with the second option. If a and b were 2 and 3, their GCF would have been 1. How is second option still sufficient? Please explain!

Thanks!
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Which of the following could be the greatest common factor of positive [#permalink]

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New post 31 May 2017, 20:42
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sasidharrs wrote:
The GCF of 4,10 is 2, which does not fall into any of the 3 categories right?


csaluja wrote:
Hi,

I am confused with the second option. If a and b were 2 and 3, their GCF would have been 1. How is second option still sufficient? Please explain!

Thanks!


Notice that the question asks "Which of the following COULD be the greatest common factor of positive integers a and b?" NOT "Which of the following MUST be the greatest common factor of positive integers a and b?"
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Re: Which of the following could be the greatest common factor of positive [#permalink]

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New post 01 Jun 2017, 06:58
Bunuel wrote:
sasidharrs wrote:
The GCF of 4,10 is 2, which does not fall into any of the 3 categories right?


csaluja wrote:
Hi,

I am confused with the second option. If a and b were 2 and 3, their GCF would have been 1. How is second option still sufficient? Please explain!

Thanks!


Notice that the question asks "Which of the following COULD be the greatest common factor of positive integers a and b?" NOT "Which of the following MUST be the greatest common factor of positive integers a and b?"


I see now, makes a lot of sense! Thanks a lot Bunuel!!
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Re: Which of the following could be the greatest common factor of positive [#permalink]

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New post 18 Jun 2017, 04:17
I took the two positive integers to be 0 and 2.

Proves right across all the three cases,

hence E
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Re: Which of the following could be the greatest common factor of positive [#permalink]

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New post 04 Dec 2017, 13:55
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Hi All,

We're told that A and B are positive integers. We're asked which of the Roman Numerals COULD be the Greatest Common Factor of A and B. We can solve the problem by TESTing VALUES.

I. 1

IF A=1 and B=2, then the GCF = 1. Roman Numeral 1 COULD be true.
Eliminate Answers A and D.

II. A

IF A=1 and B=2, then the GCF = 1 (so the GCF = A). Roman Numeral 2 COULD be true.
Eliminate Answer C.

III. A - B

IF A=2 and B=1, then the GCF = 1 (so the GCF = A-B). Roman Numeral 3 COULD be true.
Eliminate Answer B.

Final Answer:
[Reveal] Spoiler:
E


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Re: Which of the following could be the greatest common factor of positive [#permalink]

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New post 11 Jan 2018, 14:49
pepo wrote:
Which of the following could be the greatest common factor of positive integers a and b?

I. 1
II. a
III. a-b

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III


Let’s analyze each Roman numeral.

I. 1

If a = 4 and b = 7, then their greatest common factor is 1. So I is possible.

II. a

If a = 4 and b = 8, then their greatest common factor is 4, which is a. So II is possible.

III. a - b.

If b = 8 and a = 4, then their greatest common factor is 4, which is a - b. So III is possible.

Answer: E
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Which of the following could be the greatest common factor of positive [#permalink]

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New post 11 Jan 2018, 15:22
pepo wrote:
Which of the following could be the greatest common factor of positive integers a and b?

I. 1
II. a
III. a-b

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III


The main thing to notice is COULD

1. Can it be 1? Yes if both the numbers are prime
2 Can it be a? Yes is a=2 and b=4 ..GCF is 2
3. Can it be a-b? Yes, if a=8 and b=4. the GCF is 4. a-b is also equal to 4
Which of the following could be the greatest common factor of positive   [#permalink] 11 Jan 2018, 15:22
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