IDNLearn.com offers a reliable platform for finding accurate and timely answers. Ask your questions and get detailed, reliable answers from our community of experienced experts.

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).