GCF

[MBA.Aspirant]

If c and d are positive integers and m is the greatest common factor of c and d, then m must be the GCF of c and which of the following integers?

A) c + d
B) 2+d
C) cd
D) 2d
E) d^2

[Brent@GMATPrepNow]

If c and d are positive integers and m is the greatest common factor of c and d, then m must be the GCF of c and which of the following integers?

A) c + d
B) 2+d
C) cd
D) 2d
E) d^2

A quick way here is to choose numbers and eliminate incorrect answers.

If c=4 and d=2, then m=2 (since m is the GCD of c and d)

Now check the answer choices using c=4, d=2 and m=2:

A) Is m the GCD of c and c+d? Yes. 2 is the GCD of 4 and 6 (keep it)
B) Is m the GCD of c and 2+d? NO. 2 is not the GCD of 4 and 4 (eliminate it)
C) Is m the GCD of c and cd? NO. 2 is not the GCD of 4 and 8 (eliminate it)
D) Is m the GCD of c and 2d? NO. 2 is not the GCD of 4 and 4 (eliminate it)
E) Is m the GCD of c and d^2? NO. 2 is not the GCD of 4 and 4 (eliminate it)

So, the answer must be A

Cheers,
Brent

[GmatMathPro]

If m divides c and d, then c and d are multiples of m. That is c=ma and d=mb for some integers a and b. c+d=ma+mb=m(a+b), so clearly c+d is divisible by m. So m is a common factor of c and c+d. The only question is where it is the GREATEST common factor. Let x be any other common factor of c and c+d. This means that x divides c as well as c+d. But if x divides BOTH c and c+d, then it must also divide d. But if x divides c and d, it is a common factor of c and d and by definition must be less than or equal to the greatest common factor, m.

Thus, the gcf of c and c+d is m.

[Jeff@TargetTestPrep]

If c and d are positive integers and m is the greatest common factor of c and d, then m must be the GCF of c and which of the following integers?

A) c + d
B) 2+d
C) cd
D) 2d
E) d^2

Let's let c = 4 and d = 6, so m = GCF(4, 6) = 2. Let's analyze each choice.

A. c + d = 10, and GCF(4, 10) = 2, so A could be the answer.

B. 2 + d = 8, and GCF(4, 8) = 4, so B could not be the answer.

C. cd = 24, and GCF(4, 24) = 4, so C could not be the answer.

D. 2d = 12, and GCF(4, 12) = 4, so D could not be the answer.

E. d^2 = 36, and GCF(4, 36) = 4, so E could not be the answer.

Answer: A