Question

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

Answer 1

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

1. **Find the GCF of the numerical coefficients:**
- The coefficients are 45 and 15.
- The factors of 45 are \( 1, 3, 5, 9, 15, 45 \).
- The factors of 15 are \( 1, 3, 5, 15 \).
- The greatest common factor of 15 and 45 is 15.

2. **Find the GCF of the variables:**
- For \( a^2 \) and \( a \), the lowest power of \( a \) is \( a^{\min(2, 1)} = a^1 = a \).
- For \( b \) and \( b \), the lowest power of \( b \) is \( b^{\min(1, 1)} = b^1 = b \).

3. **Combine the results:**
- The GCF of the numerical part is 15.
- The GCF of the variable part is \( ab \).

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

Thus, the greatest common factor is \( \boxed{15ab} \).