Which of the following cannot be the greatest common divisor

[Jason.tuyj]

Which of the following cannot be the greatest common divisor of two postive integers x and y?

a:1
b:x
c:y
d:x-y
e:x+y

[jnelson0612]

Jason, test some values for x and y and let us know if you can make any eliminations.

[Milanproda1]

I chose random numbers 4 and 8 because I thought that it would be easier to prove the question wrong if I chose simple variables.

(a)- the gcf of of 4 and 8 is 4. the GCF cannot be 1.

(b) if x=4, then the gcf of 4 and 8 is 4. X could be a factor.

(c) if y=4, then the gcf of 4 and 8 is 4. Y could be a factor

(d) x+y=12. 12 cannot be the GCF of the two numbers that are less than 12. This is my answer choice.

(e) x-y can be either -4 or 4, in which case 4 could be the gcf of 4 and 8.

Feel free to destroy my answer choices, I feel like I did not do too well on this one.

[messi10]

Hi,

I agree with Milanproda, my answer is also D

One small clarification:

A) 1 - When two numbers do not have any prime factors in common, their GCF is 1. e.g. - 11 and 17 have a GCF of 1

Regards

Sunil

[jnelson0612]

Just to be clear, the answer is x+y. Jason lists that as E but Sunil and prada list it as D. The number testing method is quite effective with this one.