Question

What is the greatest common factor of 45a2b
and 15ab
?(1 point)

Answer 1

To find the greatest common factor (GCF) of the expressions \( 45a^2b \) and \( 15ab \), we can break it down into its constituent parts.

1. **Numerical coefficients**:
- The numerical coefficients are 45 and 15.
- The GCF of 45 and 15 can be found by determining their prime factorizations:
- \( 45 = 3^2 \times 5 \)
- \( 15 = 3 \times 5 \)
- The GCF of the coefficients is the product of the smallest powers of common prime factors:
- The minimum power of \( 3 \) is \( 3^1 \).
- The minimum power of \( 5 \) is \( 5^1 \).
- Therefore, \( \text{GCF}(45, 15) = 3^1 \times 5^1 = 15 \).

2. **Variable parts**:
- For the variables, compare \( a^2 \) and \( a^1 \) (from \( ab \)):
- The GCF is \( a^{\min(2, 1)} = a^1 = a \).
- For \( b^1 \) (in both expressions), the GCF is:
- The GCF is \( b^{\min(1, 1)} = b^1 = b \).

Now, we combine the GCF of the coefficients with the GCF of the variables:

\[
\text{GCF}(45a^2b, 15ab) = 15 \cdot a \cdot b = 15ab
\]

Thus, the greatest common factor of \( 45a^2b \) and \( 15ab \) is **\( 15ab \)**.