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Tasha believes that she can rewrite the diffrence 120 - 36 as a product of the GCF of the two numbers and another diffrence.Is she correct?

Tasha Believes That She Can Rewrite The Diffrence 120 36 As A Product Of The GCF Of The Two Numbers And Another DiffrenceIs She Correct class=

Sagot :

She is correct.
120-36=84=2^2*3*7
The key is to notice that if the two numbers are a and b, then gcf(a,b) | a-b ---> this means that the greatest common factor of a and b divides their difference. Also,    a-b> gcf(a,b)
So, the only case to consider is if gcf(a,b)=2 and a-b=42.
This is clearly possible to find 2 such numbers a,b (one example would be 62 and 20).
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