Tasha believes that she can rewrite the difference \(120 - 36\) as a product of the greatest common factor (GCF) of the two numbers and another difference. Is she correct? Explain.

She is correct. Allow me to illustrate with an illustrative example:
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36 .
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120 .
The common factors are 1, 2, 3, 4, 6, and 12 .
The greatest one is 12 .
36 = 12 x 3
120 = 12 x 10
So (120 - 36) = (12 x 10) - (12 x 3) and that's 12 (10 - 3) .

Answered by AL2006 | 2024-06-10

Tasha is correct that she can rewrite the difference 120 − 36 as a product using the GCF. The GCF of 120 and 36 is 12, allowing for the expression to be rewritten as 12 ( 10 − 3 ) . This application of the distributive property demonstrates the correct factoring of the difference.
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Answered by AL2006 | 2025-06-13