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, list all the terms explicitly.
2. Factor each term into its prime factors, including both numerical coefficients and variable parts. For example, express numbers as products of primes and variables with their exponents.
3. Compare the factorizations of all terms to find the common factors. The GCF will include the lowest powers of all common prime factors and variables present in every term.
4. Write the GCF by multiplying all the common prime factors and variables found in the previous step.
5. Verify the GCF by dividing each original term by the GCF to ensure the result is an integer or a simplified term without common factors.