greatest common divisor

[orel]

what is the greatest common divisor of positive integers m and n?
(1) m is a prime number
(2) 2n=7m

please, help!

[mals24]

IMO C

St 1 m is prime.
m =3 n = 4 GCD = 1
m = 2 n = 4 GCD = 2
So since we don't have information about n---INSUFF

St 2 2n = 7m
m = 4, n = 14 GCD = 2
m = 2, n = 7 GCD = 1

Combining 1&2
m is prime.
The only prime number that will satisfy St 2 is 2
So m=2, n=7 GCD =1

C

[rohangupta83]

IMO C

St 1 m is prime.
m =3 n = 4 GCD = 1
m = 2 n = 4 GCD = 2
So since we don't have information about n---INSUFF

St 2 2n = 7m
m = 4, n = 14 GCD = 2
m = 2, n = 7 GCD = 1

Combining 1&2
m is prime.
The only prime number that will satisfy St 2 is 2
So m=2, n=7 GCD =1

C

can GCD actually be 1?

[scoobydooby]

yes for numbers that are prime to each other

[mals24]

can GCD actually be 1?

Yes like scoobydooby said, GCD of all prime numbers is 1.

2 = 2*1
7 = 7*1

The highest common factor of 2 and 7 is 1.

[austin]

GCD of 2 numbers (x,y) is the greatest/biggest number that can divide both x and y.

(x,y) GCD/HCF

2,3 1
4,5 1

RESULT: The HCF of two consectutive positive numbers is 1

2,5 1
7,23 1

RESULT: The HCF of two prime numbers is 1

IF THE HCF OF TWO NUMBERS IS 1, THEN THE TWO NUMBERS ARE CO-PRIME ie. 2 and 3 are co-prime.

Hope I have given some clarity...

[rohangupta83]

can GCD actually be 1?

Yes like scoobydooby said, GCD of all prime numbers is 1.

2 = 2*1
7 = 7*1

The highest common factor of 2 and 7 is 1.

I agree with C then

good to have concepts refreshed

[cramya]

One more vote for C) approach same as Mals24.


GCD : 1 (for any 2 primes this is the gcd)