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A
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Difficulty:
85%
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Question Stats:
24% (01:00) correct
76%
(00:50)
wrong
based on 237
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What is the greatest common divisor of two positive integers a and b?
(1) a and b share exactly one common factor.
(2) a and b are both prime numbers.
(1) a and b share exactly one common factor.
(2) a and b are both prime numbers.
21 Dec 2009, 12:16
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What is the greatest common divisor of two positive integers a and b?
(1) a and b share exactly one common factor --> since 1 is the common factor for all integers, and since given that a and b share only one common factor, then the greatest common divisor of a and b must be 1. Sufficient.
(2) a and b are both prime numbers. Two different primes share only 1 as a common factors, but as a could be equal to b, greatest common factor could be a (b) in this case. Hence insufficient.
Answer: A.
(1) a and b share exactly one common factor --> since 1 is the common factor for all integers, and since given that a and b share only one common factor, then the greatest common divisor of a and b must be 1. Sufficient.
(2) a and b are both prime numbers. Two different primes share only 1 as a common factors, but as a could be equal to b, greatest common factor could be a (b) in this case. Hence insufficient.
Answer: A.
21 Dec 2009, 13:13
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If both numbers are prime, don't we then know that 1 is the greatest common divisor by definition? Isn't II) saying the same thing as I)?
