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

Question

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

Bunuel · Accepted Answer

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.

Raahan · Answer

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

Bunuel · Answer

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.

Shiv2016 · Answer

Bunuel

In the third case (a-b), a and b can also be 6 and 4?

Bunuel · Answer

Yes. The greatest common factor of 6 and 4 is 2.

sasidharrs · Answer

The GCF of 4,10 is 2, which does not fall into any of the 3 categories right?

JS1290 · Answer

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!

Bunuel · Answer

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 ?"

JS1290 · Answer

I see now, makes a lot of sense! Thanks a lot Bunuel!!

hdwnkr · Answer

I took the two positive integers to be 0 and 2.

Proves right across all the three cases,

hence E

EMPOWERgmatRichC · Answer

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:  E

GMAT assassins aren't born, they're made, 
Rich

ScottTargetTestPrep · Answer

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

Turkish · Answer

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

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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

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