14 is the GCF of a number M and 210. What are possible values of M?

1 Answer
Oct 8, 2016

Possible values of M are #{14xx1,14xx2,14xx4,14xx7,...}#

Explanation:

Prime factors of #210# are #2xx3xx5xx7# and factors are

#{1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210}#

As #14# is the GCF, number has to be a multiple of #14#.

Further, its multiple cannot have #3# an #5# as it factor, i.e. all multiples of #14#, which have #3# and #5#.too as factors are to be avoided among multiples of #14# i.e..#{14xx1,14xx2,14xx4,14xx7,...}#

Hence, possible values of M are #{14,28,56,98,112,...........}#
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