Yep, I guess I had a temporary mind block & got completely stuck. Only 20x CANNOT be a divisor of 35x & 20y, because 35x/20x is not an integer.tohellandback wrote:
A) agreed as you said
B) take the example x=21,y=14
35x=5*7*3*7
20y=4*5*2*7
GCF is 5*7 (7 is 21-14, thats what I meant when i said "depends upon the values of x and y")
C) Hold on I will give you a "big explanation"
D) possible because it is possible that between two numbers one of them can be the GCF.
I will give you an example, you figure out the rest.
y=3
=12
well, let me explain
since 20y contains 2^2, 5 and y. it can be the GCF if 35x contains all of these. now 35x already has 5 so, any value of x that contains 2^2 and as factors will make it possible
E) same explanation as above
20y already contains 5. so any value of y that has x and 7 as factors will make it possible
ex: x=3
y=21
by now I think you have understood why C is right, but still
35x=5*7*x
20x would have been possible only if there was a 2^2 in the factorization.
now you can argue that what if x has that 2^2 so precious to me
let x=4
now 20x is 2^2*5*2^2
but you original number 35x doesn't have two (2^2)s. It has only one 2^2 and that is from x. so 20x cannot divide it. Now you see why i mentioned there should be the prime numbers in the factorization.
Hope I am clear. Thanks
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