akshatgupta87 wrote:Can someone explain, how to tackle this type of question.
Target2009 wrote:
GCF ( 16, n) = 4 i.e n is max multiple of 4
GCF (45, n) = 3 i.e n is also multiple of 3 but not multiple of 5.
GCF( 210, n) = ( 210=2*3*5*7 , n=2*2*3*...) GCF = 2 * 3* 7 ( but not 5 as per 2nd statement) = 42
Hi there!
Target2009´s reasoning is very good, but let me "structure" the whole thing a bit more, for us to be able to obtain everything the info given let us conclude about the positive integer n !
01. From GCF(16=2^4,n)=4 we may conclude that n=4M, where M is a positive ODD integer (why?);
02. From GCF(45=3^2*5,4M)=3 we may conclude that M=3K, where K is positive ODD integer (because of M) that is not a multiple of 3 nor a multiple of 5 (why?) ;
Combining the info above, we know that n=12K, where K is a positive ODD integer that is not a multiple of 3 nor a multiple of 5... what about GCF(210=2*3*5*7,n) ?
GCF(210=2*3*5*7,n)= GCF(2*3*5*7,2^2*3*K where K...) = 2*3*W, where W is a positive integer equal to 1 or to 7, therefore there are only two possibilities for GCF(210,n), they are: 6 and 42.
I hope you enjoy this discussion.
Regards,
Fabio.
