Questions: Find the GCF (greatest common factor) of the following terms. 77 x^2, 55,9

Solution Steps

We are given the terms \( 77x^2 \), \( 55 \), and \( 9 \). To find the greatest common factor (GCF), we will first consider the numerical coefficients of these terms: \( 77 \), \( 55 \), and \( 9 \).

Next, we perform the prime factorization of each number:

• \( 77 = 7 \times 11 \)
• \( 55 = 5 \times 11 \)
• \( 9 = 3^2 \)

Now, we identify the common prime factors among the factorizations:

• The prime factors of \( 77 \) are \( 7 \) and \( 11 \).
• The prime factors of \( 55 \) are \( 5 \) and \( 11 \).
• The prime factors of \( 9 \) are \( 3 \).

The only common prime factor among \( 77 \), \( 55 \), and \( 9 \) is \( 11 \).

Since \( 11 \) is the only common factor, and it appears in the factorizations of \( 77 \) and \( 55 \) but not in \( 9 \), the GCF of the terms \( 77 \), \( 55 \), and \( 9 \) is \( 1 \).

Final Answer