Which statements about the factors of the terms in the expression 20 a + 15 a b + 24 b are true? Select three options.

Question

The factors common to 20a and 15ab are 1, 5, a, and b.
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 ab.
The GCF of the expression is 1

Answer 1

To analyze the expression \(20a + 15ab + 24b\), let's break it down and identify the greatest common factors (GCF).

1. 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 \(1, 2, 3, 4, 6, 8, 12, 24, b\).

2. Common factors:

   • Between \(20a\) and \(15ab\): The common factors are \(1, 5, a\).
   • Between \(20a\) and \(24b\): The common factors are \(1, 2, 4\).

3. 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:

1. The factors common to \(20a\) and \(15ab\) are \(1, 5, a\).
2. The factors common to \(20a\) and \(24b\) are \(1, 2, 4\).
3. 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 \(1\).