To find the Greatest Common Factor (GCF), what must you do with the integers?

To find the Greatest Common Factor (GCF), what must you do with the integers?

• A. Add both integers together
• B. Break them down into their prime factorizations
• C. Multiply both integers directly
• D. Subtract the smaller from the larger

Answer: (B)

To find the Greatest Common Factor (GCF) of two integers, breaking them down into their prime factorizations is the key step. Prime factorization involves expressing each integer as a product of its prime numbers. Once both integers are expressed in this form, the next step is to identify the common prime factors that appear in both factorizations. The GCF is then determined by multiplying those common prime factors together. This approach effectively highlights the largest factor that both integers share, which is the definition of the greatest common factor. Utilizing prime factorization ensures that no factors are overlooked in the process, making it a comprehensive method for finding the GCF. The other methods mentioned, such as adding the integers, multiplying them, or subtracting one from the other, do not provide a reliable way to identify the greatest common factor, as they do not focus on the underlying divisors that both numbers share. Thus, using prime factorization is the best method for accurately determining the GCF.

To find the Greatest Common Factor (GCF) of two integers, breaking them down into their prime factorizations is the key step. Prime factorization involves expressing each integer as a product of its prime numbers. Once both integers are expressed in this form, the next step is to identify the common prime factors that appear in both factorizations.

The GCF is then determined by multiplying those common prime factors together. This approach effectively highlights the largest factor that both integers share, which is the definition of the greatest common factor. Utilizing prime factorization ensures that no factors are overlooked in the process, making it a comprehensive method for finding the GCF.

The other methods mentioned, such as adding the integers, multiplying them, or subtracting one from the other, do not provide a reliable way to identify the greatest common factor, as they do not focus on the underlying divisors that both numbers share. Thus, using prime factorization is the best method for accurately determining the GCF.