Is the integer z devisible by 6?
(1) The greatest common factor of z and 12 is 3.
(2) The greatest common factor of z and 15 is 15.
Can someone please sovle this one, and explain the basic rules and how to proceed?
Thanks!
Greatest common factor
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(2) The GCF of z & 15 is 15 (5x3), so z is a mulitple of 15. Maybe 30, 45 etc.
30 is divisible by 6 but not 45 . Not sufficient.
(1) The GCF of z & 12 (2 x 2x 3) is 3.
z does not have a factor 2 , in that case the GCF should be 6 not 3, cos 12 has a factor 2.
Take the example 45(3x3x5) and 12(2x2x3) the GCF is 3 not 6.
Sufficient to say z is not divisible by 6.
IMO A
30 is divisible by 6 but not 45 . Not sufficient.
(1) The GCF of z & 12 (2 x 2x 3) is 3.
z does not have a factor 2 , in that case the GCF should be 6 not 3, cos 12 has a factor 2.
Take the example 45(3x3x5) and 12(2x2x3) the GCF is 3 not 6.
Sufficient to say z is not divisible by 6.
IMO A
Hi,
Can you explain why st 1 is sufficient? I'm confused. I was thinking this way:-
if Z is to be divisible by 6(3x2), it needs to have both 3 and 2 in the prime factorization.
1. gcf of z and 12 is 3
12 - 3 x 2 x 2
z - 3 x ? x ?...
can i say that z is a multiple of 3, like you said for st 2 (z is multiple of 15)?
so if z is a multiple of 3, then z may be 6 or z may be 9. which is insufficient for 1. This is what I'm thinking. Could you give another explanation to help me understand where I'm seeing things wrongly?
Can you explain why st 1 is sufficient? I'm confused. I was thinking this way:-
if Z is to be divisible by 6(3x2), it needs to have both 3 and 2 in the prime factorization.
1. gcf of z and 12 is 3
12 - 3 x 2 x 2
z - 3 x ? x ?...
can i say that z is a multiple of 3, like you said for st 2 (z is multiple of 15)?
so if z is a multiple of 3, then z may be 6 or z may be 9. which is insufficient for 1. This is what I'm thinking. Could you give another explanation to help me understand where I'm seeing things wrongly?
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Hi Kstv:
If I applied the same logic in (1) as in (2), I would have:
(2) The GCF of z & 15 is 15 (5x3), so z is a mulitple of 15. Maybe 30, 45 etc.
30 is divisible by 6 but not 45 . Not sufficient. -- This is correct, I agree
(1) The GCF of z & 12 (2 x 2x 3) is 3.
z does not have a factor 2 , in that case the GCF should be 6 not 3, cos 12 has a factor 2.
Take the example 45(3x3x5) and 12(2x2x3) the GCF is 3 not 6.
Sufficient to say z is not divisible by 6.
About (1), I could say that z is multiple of 3, which could be 12, or 15. 12 is divisible by 6 (has a factor of 2), but not 15, so not suficient.
What am I doing wrong??
Thanks,
Silvia
If I applied the same logic in (1) as in (2), I would have:
(2) The GCF of z & 15 is 15 (5x3), so z is a mulitple of 15. Maybe 30, 45 etc.
30 is divisible by 6 but not 45 . Not sufficient. -- This is correct, I agree
(1) The GCF of z & 12 (2 x 2x 3) is 3.
z does not have a factor 2 , in that case the GCF should be 6 not 3, cos 12 has a factor 2.
Take the example 45(3x3x5) and 12(2x2x3) the GCF is 3 not 6.
Sufficient to say z is not divisible by 6.
About (1), I could say that z is multiple of 3, which could be 12, or 15. 12 is divisible by 6 (has a factor of 2), but not 15, so not suficient.
What am I doing wrong??
Thanks,
Silvia
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IF GCF of z and 12 is 3 means that z is not a multiple of 2 and hence cannot be divisible by 6.
IMO A
IMO A
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See the q (1) The greatest common factor of z and 12 is 3.ssuarezo wrote:Hi Kstv:
If I applied the same logic in (1) as in (2), I would have:
About (1), I could say that z is multiple of 3, which could be 12, or 15. 12 is divisible by 6 (has a factor of 2), but not 15, so not suficient.
What am I doing wrong??
Thanks,
Silvia
but you are considering z = 12 this is wrong
even then if z was 12 the factor of 2 you mention will make the GCF 3 X 2 X 2
The Q stem 1 says the GCF is 3 so z cannot be an even no.