To analyze the expression \(20a + 15ab + 24b\), let's break it down and identify the greatest common factors (GCF).
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Factors of each term:
- 20a: The factors are \(1, 2, 4, 5, 10, 20, a\).
- 15ab: The factors are \(1, 3, 5, 15, a, b\).
- 24b: The factors are \(1, 2, 3, 4, 6, 8, 12, 24, b\).
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Common factors:
- Between \(20a\) and \(15ab\): The common factors are \(1, 5, a\).
- Between \(20a\) and \(24b\): The common factors are \(1, 2, 4\).
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Finding the GCF:
- The GCF for the entire expression \(20a + 15ab + 24b\) is determined by identifying the common factors among all terms. The common factors for all three terms include \(1\) (as all coefficients have \(1\) as a factor), but there is no other factor common to all terms. Therefore, the GCF of the entire expression is 1.
Therefore, the true statements are:
- The factors common to \(20a\) and \(15ab\) are \(1, 5, a\).
- The factors common to \(20a\) and \(24b\) are \(1, 2, 4\).
- The GCF of the expression is \(1\).
The chosen correct options are:
- The factors common to \(20a\) and \(15ab\) are \(1, 5,\) and \(a\).
- The factors common to \(20a\) and \(24b\) are \(1, 2,\) and \(4\).
- The GCF of the expression is \(1\).