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 all the terms 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$, factor it as \(2 \times 2 \times 3 \times x^3 \times y\).
3. List the common factors that appear in all terms. This includes the prime numbers and variables with the smallest exponent that appear in every term.
4. Multiply these common factors together to find the GCF. Remember to include the variables with the lowest powers common to all terms.
5. Express the GCF as a product of the common numerical factors and variables. This expression represents the greatest factor that divides all the terms without leaving a remainder.