What is the greatest common factor of the following lists of numbers?
$19,57$

• A. $3$
• B. $57$
• C. $19$
• D. $1$

Answer: (C)

Verified step by step guidance

1. Identify the terms given in the problem. Since the problem is about finding the Greatest Common Factor (GCF) of terms, first write down each term clearly.
2. Factor each term into its prime factors, including both numerical coefficients and variables with their exponents. For example, if a term is \$12x^3y^2$, factor it as \(2 \times 2 \times 3 \times x^3 \times y^2\).
3. Compare the prime factorizations of all terms to find the common factors. For numerical coefficients, find the common prime numbers. For variables, find the lowest power of each variable that appears in all terms.
4. Multiply all the common prime factors and variables with their lowest exponents together to form the GCF. This product represents the greatest factor that divides all the terms exactly.
5. Write the GCF as a simplified expression combining the numerical part and the variable part. This is the final expression representing the Greatest Common Factor of the given terms.