Question

Identify the greatest common factor of 28b^2c^2 and 21ab^2

Answer 1

To find the greatest common factor (GCF) of the expressions \(28b^2c^2\) and \(21ab^2\), we will first factor each expression into its prime factors along with the variable factors.

1. **Factor the coefficients:**
- For \(28\):
\[
28 = 2^2 \times 7
\]
- For \(21\):
\[
21 = 3 \times 7
\]

2. **Identify the GCF of the coefficients:**
- The only common prime factor is \(7\). Thus, the GCF of the coefficients \(28\) and \(21\) is \(7\).

3. **Factor the variable parts:**
- From \(28b^2c^2\), we have \(b^2\) and \(c^2\).
- From \(21ab^2\), we have \(a\) and \(b^2\).

4. **Identify the GCF of the variable parts:**
- The variable \(b^2\) is common in both terms.
- The other variables \(a\) and \(c^2\) do not appear in both expressions.

5. **Combine the GCFs:**
- The GCF of the coefficients is \(7\).
- The GCF of the variable parts is \(b^2\).

Thus, the overall GCF of \(28b^2c^2\) and \(21ab^2\) is:
\[
\text{GCF} = 7b^2
\]

So, the greatest common factor of \(28b^2c^2\) and \(21ab^2\) is \(\boxed{7b^2}\).