HCF
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1)=> j and k are consecutive integers. the GCF of two consecutive integers is 1. sufficient
2) if j=k=10, GCF=10; if j=3 and k=5, GCF is 1. no unique CF obtained. not sufficient.
2) if j=k=10, GCF=10; if j=3 and k=5, GCF is 1. no unique CF obtained. not sufficient.

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scoobydooby wrote:1)=> j and k are consecutive integers. the GCF of two consecutive integers is 1. sufficient
2) if j=k=10, GCF=10; if j=3 and k=5, GCF is 1. no unique CF obtained. not sufficient.
Tip 1: when 2 numbers have GCD as 1, its called co primes!
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For clarification as to why two consecutive integers must have a GCF of 1:
If the GCF of two different numbers were 2, for example, both numbers would be even, and thus at least a distance of 2 apart.
If the GCF of two different numbers were 3, both numbers would be multiples of 3, and thus at least a distance of 3 apart.
So in general, if the GCF of two different numbers were N, both numbers would be multiples of N, and thus at least a distance of N apart.
Therefore, if two numbers are consecutive integers (and thus a distance of 1 apart), they cannot have a GCF of anything higher than 1.
If the GCF of two different numbers were 2, for example, both numbers would be even, and thus at least a distance of 2 apart.
If the GCF of two different numbers were 3, both numbers would be multiples of 3, and thus at least a distance of 3 apart.
So in general, if the GCF of two different numbers were N, both numbers would be multiples of N, and thus at least a distance of N apart.
Therefore, if two numbers are consecutive integers (and thus a distance of 1 apart), they cannot have a GCF of anything higher than 1.
Rich Zwelling
GMAT Instructor, Veritas Prep
GMAT Instructor, Veritas Prep