What is the greatest common factor of the following sets of monomials?
$30m^3{n}^2,45m^2{n}^4,75m^4{n}^3$

• A. $5m^2{n}^2$
• B. $15m^2{n}^2$
• C. $450m^4{n}^3$
• D. $15$

Answer: (B)

Verified step by step guidance

1. Identify the terms given in the problem. Since the problem is about finding the GCF (Greatest Common Factor) 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 prime factors of each term side by side to compare them easily.
4. Determine the common factors that appear in every term. For numerical coefficients, find the greatest number that divides all coefficients. For variables, take the variable with the smallest exponent that appears in all terms.
5. Multiply all the common prime factors and variables together to write the GCF in its simplest form.