PS: GCD

[cesar.rodriguez.blanco]

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

I missed this question. Can m=n?

[selva.e]

i dont think m = n since both are integers.

1) m is prime INSUFF. didn't tell anything about n .

2) 2n = 7m
this tells something about m and n.

but n will be multiple of 7 and m will muliples of 2. to make aboev stmt true. So we get infinite GCD. insuff.

combine both,

if m is prime, then it should be 2, to make the 2n = 7m true.
So if m = 2, then n = 7

so gcd(2,7) can be found. SO C.

[RonPurewal]

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

I missed this question. Can m=n?

(1)
you should still find the values that prove this statement insufficient.

if m = 3 (which is prime) and n = 6, then the gcf is 3.
if m = 3 (which is prime) and n = 5, then the gcf is 1.
insufficient.

(2)

if you have a statement like this - number * variable = other number * other variable - then you should recognize it as a RATIO.
to change it into RATIO form, divide by one of the numbers, and divide by the other variable (i.e., the variable that doesn't have this number as a coefficient).

in the case of this statement, you can divide by 2m on both sides, to give n/m = 7/2. (you could also divide by 7n, to give m/n = 2/7.)

so, the ratio of n to m is 7:2.
if they're actually 7 and 2, the gcf is 1.
if they're multiples of these numbers, then the gcf is not 1. (for instance, if they're 14 and 4, the gcf is 2.)
insufficient.

--

(together)
if you need a prime, and the ratio is 7 to 2, then the numbers must actually be 7 and 2.
sufficient.

[bawies00]

Is it not possible to say, when using statement 2 only, that the GCF will be 1/2*m ?

[tim]

sure. and since you don't know what m is, the statement is insufficient..

[rkafc81]

Is it not possible to say, when using statement 2 only, that the GCF will be 1/2*m ?

hey sorry don't get how you came to this GCF value?
can you please explain

thanks

[tim]

sure. if 2n = 7m, then n must be a multiple of 7 and m must be a multiple of 2. let n = 7q and m = 2p. now the equation looks like this:

2*7q = 7*2p

oh, this means that p = q, so n = 7p and m = 2p. the GCF of m and n is therefore p, which is equal to m/2 because m = 2p..

[rachelhong2012]

dear instructors,

in order to find out the LCM of two variables/numbers, we have to know all of their primes, am I right?



in this case, we can infer from 2n=7m that n must have 7 as its prime and m must have 2 as its prime, thus their LCM include AT LEAST a 2 and a 7, but we don't know what other common factors they share, thus we don't know what else is in their LCM.

Thanks!

[jnelson0612]

dear instructors,

in order to find out the LCM of two variables/numbers, we have to know all of their primes, am I right?



in this case, we can infer from 2n=7m that n must have 7 as its prime and m must have 2 as its prime, thus their LCM include AT LEAST a 2 and a 7, but we don't know what other common factors they share, thus we don't know what else is in their LCM.

Thanks!

Correct! We need the knowledge that m is prime, as given in statement 1, to know that n is in fact 7 and m is in fact 2.