Question

What is the greatest common factor of 18a4b3
and 21a8b3
?

Answer 1

To find the greatest common factor (GCF) of \(18a^4b^3\) and \(21a^8b^3\), we start by determining the GCF of the numerical coefficients and then the GCF of each variable part.

1. **Numerical Coefficients:**
- The coefficients are 18 and 21.
- The prime factorization of 18 is:
\[
18 = 2 \times 3^2
\]
- The prime factorization of 21 is:
\[
21 = 3 \times 7
\]
- The common factor from the prime factorizations is \(3\).

2. **Variable Part:**
- For \(a^4\) and \(a^8\), the GCF is the variable raised to the lowest exponent:
\[
\text{GCF}(a^4, a^8) = a^{\min(4, 8)} = a^4
\]
- For \(b^3\) in both terms, since they are the same, the GCF is:
\[
\text{GCF}(b^3, b^3) = b^3
\]

3. **Combine the GCFs:**
- Combining all these, we get:
\[
\text{GCF}(18a^4b^3, 21a^8b^3) = 3 \cdot a^4 \cdot b^3
\]

Thus, the greatest common factor of \(18a^4b^3\) and \(21a^8b^3\) is:
\[
\boxed{3a^4b^3}
\]