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# What is the greatest common divisor of positive integers m

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What is the greatest common divisor of positive integers m [#permalink]  23 Nov 2008, 12:07
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What is the greatest common divisor of positive integers m and n?

1) m is a prime number

2) 2n = 7m
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Re: DS: Divisor [#permalink]  23 Nov 2008, 12:34
2
KUDOS
What is the greatest common divisor of positive integers m and n?
1) m is a prime number
2) 2n = 7m

1) GCD can be 1 or m => insuff
2) can be any even m's => insuff
e.g. 2x14 = 7x4 ; GCD:2
e.g. 2x21 = 7x6 ; GCD:3

if GCD is m, then n/m = integer, but n/m=7/2
=> GCD is 1
together suff => C
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Re: DS: Divisor [#permalink]  24 Nov 2008, 12:36
I'm confused between C and E.

I pick C as 1 is common divisior
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Re: DS: Divisor [#permalink]  24 Nov 2008, 23:09
C.
(1) and (2) are clearly insufficient.
combining If 2n=7m and m is a prime, then m has to be 2.(2 is only even prime number) and GCD will be 1.
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Re: DS: Divisor [#permalink]  25 Nov 2008, 07:35
What is the greatest common divisor of positive integers m and n?

1) m is a prime number

2) 2n = 7m

My choice is B.
2n=7m
n=7k
m=2k (k is an integer)
=> the greatest common divisor of m and n is k or n/7. (or m/2)
I'm not sure...
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Re: DS: Divisor [#permalink]  25 Nov 2008, 18:33
DavidArchuleta wrote:
My choice is B.
2n=7m
n=7k
m=2k (k is an integer)
=> the greatest common divisor of m and n is k or n/7. (or m/2)
I'm not sure...

but n and m can have different values, so k will keep on changing.

for example:
twilight wrote:
2)
e.g. 2x14 = 7x4 ; GCD:2
e.g. 2x21 = 7x6 ; GCD:3
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Re: DS: Divisor [#permalink]  25 Nov 2008, 19:44
What is the greatest common divisor of positive integers m and n?

1) m is a prime number
2) 2n = 7m

1: m is a prime? what about n? nsf.
2: 2n = 7m?
n could be 7 and m = 2.
n = 14 and m = 4
n = 28 and m = 8

nsf.

1 and 2: m is a prime and 7m = 2n, n must be 7 and m = 2. othert wise 2n cannot be equal to 7m.

therefore, C.
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Re: DS: Divisor [#permalink]  25 Nov 2008, 20:18
What is the greatest common divisor of positive integers m and n?

1) m is a prime number

m is prime. n can be any thing but their GCD will always be 1. The only common divisor of a prime number and any other number is 1. How ever if m=n GCD=m=n. Hence insufficient

2) 2n = 7m

n= 7m/2 means m is divisible by 2. so m can be 2, n can be 7 with GCD 1 or m =4 and n =14 and GCD =2. Hence Insufficient

Together, m is prime and 2n=7m implies means m=2. M is the only even prime. m=2 and n=7
GCD=1

C
Re: DS: Divisor   [#permalink] 25 Nov 2008, 20:18
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