Identify the greatest common factor of $$ 20 x z $$ and $$ 24 z $$

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To find the greatest common factor (GCF) of the expressions $$ 20xz $$ and $$ 24z $$, we can follow these steps:

1. **Factor each expression:**
   - For $$ 20xz $$:
     - The prime factorization of $$ 20 $$ is $$ 2^2 \times 5 $$.
     - Therefore, $$ 20xz = 2^2 \times 5 \times x \times z $$.
   - For $$ 24z $$:
     - The prime factorization of $$ 24 $$ is $$ 2^3 \times 3 $$.
     - Therefore, $$ 24z = 2^3 \times 3 \times z $$.

2. **Identify the common factors:**
   - The common factors between $$ 20xz $$ and $$ 24z $$ are the factors of $$ z $$ and the powers of $$ 2 $$.
   - The minimum power of $$ 2 $$ in both factorizations is $$ 2^2 $$.
   - The factor $$ z $$ is present in both expressions.

3. **Combine the common factors:**
   - The GCF is given by multiplying the common factors:
     $$
     \text{GCF} = 2^2 \times z = 4z
     $$

Thus, the greatest common factor of $$ 20xz $$ and $$ 24z $$ is $$ \boxed{4z} $$.
The greatest common factor of $$ 20xz $$ and $$ 24z $$ is $$ 4z $$.

Identify the greatest common factor of \( 20 x z \) and \( 24 z \)

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