Ds - Number properties

Question

What is the greatest common factor of positive integers a and b?

(1) a = b + 4

(2) b/4 is an integer

Ravshonbek · Answer

1. a-b=4
----a=104 and b=100 so GCF=4 or a=54 and b=50 then GCF=2
not suff

2. b/4 is an integer. 
----no info about a

combined.

a and b are multiples of 4 as both are divisible by 4.
so GCF=4

C

tamg08 · Answer

I agree that 4 is a common factor, but how do you prove that is the GCF?

maratikus · Answer

let's assume x is the GCF of a and b, then a-b would be a multiple of GCF -> 4 is a multiple of GCF -> GCF can not be higher than 4

since 1&2 -> GCF is a multiple of 4

Therefore, 4 is the GCF.

Prep Toolkit