If a and b are positive integers divisible by 6, is 6 the greatest common divisor of a and b?
(1) a = 2b + 6
(2) a = 3b
S1. take b = 6, 12, 18 and any multiple of six
You will always get that six is the greatest common divisor
42 = 2(18) +6 so here six is the greatest common divisor
S2. 36 = 3(12)
here the greatest common 12 divisor is 12. Whatever the value of B is that is the greatest common divisor.
a and b are divisible by 6
(1) a=2b+6 => say b=6k k is any integer =>
a=2(6k)+6 => a=(2k+1)6
again to get the greatest common factor other than 6 here
k =2k+1=> k=-1
hence a=-6 a,b are posiive hence this is ruled out SUFFI 6 is greatest common divisor
(2)a=3b =>say b=6k a=18k k can be anything hence greatest common divisor can be any integer other than 6 too INSUFFI
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