Question

Factor Linear Expressions Practice
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Question
What is the greatest common factor of 45a2b
and 15ab
?

Answer 1

To find the greatest common factor (GCF) of the expressions \( 45a^2b \) and \( 15ab \), we need to consider both the numerical coefficients and the variable parts.

1. **Numerical Coefficient:**
- The coefficients are \( 45 \) and \( 15 \).
- The GCF of \( 45 \) and \( 15 \) is \( 15 \).

2. **Variable Part:**
- For \( a \): The first expression has \( a^2 \), and the second has \( a \). The GCF is \( a \).
- For \( b \): Both expressions have \( b^1 \), so the GCF is \( b \).

Now, we combine our findings:

- GCF of the numerical part = \( 15 \)
- GCF for \( a \) = \( a \)
- GCF for \( b \) = \( b \)

Putting it all together, the GCF of \( 45a^2b \) and \( 15ab \) is:

\[
15ab
\]

So, the greatest common factor is \( 15ab \).