Question
What is the greatest common factor of 45a2b
and 15ab
?(
and 15ab
?(
Answers
Answered by
GPT-4o mini
To find the greatest common factor (GCF) of the expressions \( 45a^2b \) and \( 15ab \), we'll break down each expression into its prime factors and variable components.
1. **Factor the coefficients:**
- \( 45 = 3^2 \times 5 \)
- \( 15 = 3 \times 5 \)
2. **Identify the variable factors:**
- The first expression has \( a^2b \).
- The second expression has \( ab \).
3. **Combine the factors:**
- For the coefficients, the GCF of \( 45 \) and \( 15 \) is \( 15 \) (as \( 15 = 3 \times 5 \)).
- For the variable \( a \), the GCF of \( a^2 \) and \( a \) is \( a \) (take the lower exponent).
- For the variable \( b \), the GCF of \( b \) and \( b \) is \( b \) (both terms have \( b \)).
4. **Combine everything:**
- The GCF of \( 45a^2b \) and \( 15ab \) is \( 15ab \).
Therefore, the greatest common factor of \( 45a^2b \) and \( 15ab \) is \( \boxed{15ab} \).
1. **Factor the coefficients:**
- \( 45 = 3^2 \times 5 \)
- \( 15 = 3 \times 5 \)
2. **Identify the variable factors:**
- The first expression has \( a^2b \).
- The second expression has \( ab \).
3. **Combine the factors:**
- For the coefficients, the GCF of \( 45 \) and \( 15 \) is \( 15 \) (as \( 15 = 3 \times 5 \)).
- For the variable \( a \), the GCF of \( a^2 \) and \( a \) is \( a \) (take the lower exponent).
- For the variable \( b \), the GCF of \( b \) and \( b \) is \( b \) (both terms have \( b \)).
4. **Combine everything:**
- The GCF of \( 45a^2b \) and \( 15ab \) is \( 15ab \).
Therefore, the greatest common factor of \( 45a^2b \) and \( 15ab \) is \( \boxed{15ab} \).