Which of the following CANNOT be the greatest common divisor of two positive integers and ?
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Wait, is (E) really impossible? What if x and y are both small? Like x=2, y=4... gcd is 2 and x+y=6, no. Hmm, but I can't find a counterexample so I guess it's right.
Got this one wrong initially. I picked (D) because I thought x-y could be negative, but the question says positive integers so... anyway, the trick with (E) is that any common divisor of x and y has to be ≤ min(x,y).
Easy one once you realize a GCD can never be bigger than either number.
Can someone explain why (C) is possible? I get that gcd(x,y) divides both, but can it actually equal y?
What it tests
Your understanding of divisibility rules, least common multiples, and greatest common factors.
Common trap
Forgetting that 1 is not prime and that every integer divides 0.