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?

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).

Answered by Tan569 | 2024-06-10

Yes, Tasha is correct. The difference 120 - 36 can be rewritten as the product of the GCF (12) and another difference (7). Therefore, 120 - 36 = 12 * 7.
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Answered by Tan569 | 2024-09-04