1. ## Greatest Common Divisor

Which of the following CANNOT be the greatest common divisor of the two positive integers x and y?

A. 1
B. x
C. y
D. x - y
E. x + y

I do not understand exactly what this question is asking?
The answer is choice E. I do not understand why E is the answer. Can someone state this question another way?

2. ## Re: Greatest Common Divisor

Originally Posted by harpazo
Which of the following CANNOT be the greatest common divisor of the two positive integers x and y?
A. 1
B. x
C. y
D. x - y
E. x + y
I do not understand exactly what this question is asking?
The answer is choice E. I do not understand why E is the answer. Can someone state this question another way?
To find the $GCF(x,y)$ write down the prime factorization of each. Then list the common factors with the least power present.
EX: $x=2^5\cdot3^5\cdot 5^3\cdot 7^4\cdot 11^5~\& ~y=2^3\cdot 7^5\cdot 11^8\cdot 13^5\cdot$ $GCF(x,y)=2^3\cdot7^4\cdot 11^5$

NOTE $GCD(x,y)\le\min\{x,y\}$

3. ## Re: Greatest Common Divisor

It's much simpler than that. Because x and y are "two positive integers", x+ y is larger than either x or y so cannot be a divisor of either one, much less a "common" divisor!

4. ## Re: Greatest Common Divisor

Originally Posted by Plato
To find the $GCF(x,y)$ write down the prime factorization of each. Then list the common factors with the least power present.
EX: $x=2^5\cdot3^5\cdot 5^3\cdot 7^4\cdot 11^5~\& ~y=2^3\cdot 7^5\cdot 11^8\cdot 13^5\cdot$ $GCF(x,y)=2^3\cdot7^4\cdot 11^5$

NOTE $GCD(x,y)\le\min\{x,y\}$