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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

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.
_________________

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?"
_________________

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

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01 Jun 2017, 05:58

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!!

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.

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

Show Tags

11 Jan 2018, 14:22

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