Question

Find the GCF of the monomials 65 p squared​, 26​pq, and 39 q squared.
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Part 1
The GCF of 65 p squared​, 26​pq, and 39 q squared is
  
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Answer 1

To find the greatest common factor (GCF) of the monomials \( 65p^2 \), \( 26pq \), and \( 39q^2 \), we need to determine the GCF of the coefficients and the common variables.

1. **Finding the GCF of the coefficients:**
- The coefficients are \( 65 \), \( 26 \), and \( 39 \).
- The prime factorization of each coefficient:
- \( 65 = 5 \times 13 \)
- \( 26 = 2 \times 13 \)
- \( 39 = 3 \times 13 \)

The common factor among these numbers is \( 13 \).

2. **Finding the GCF of the variables:**
- \( 65p^2 \) has \( p^2 \)
- \( 26pq \) has \( pq \)
- \( 39q^2 \) has \( q^2 \)

The variable \( p \) is present in the first two monomials but not in the third monomial, so it won't contribute to the GCF. The variable \( q \) is present in the second and third monomials, but the lowest power of \( q \) among the three is \( q^0 \) (which is \( 1 \) since it is not present in the first monomial).

3. **Putting it all together:**
- The GCF of the coefficients is \( 13 \).
- The GCF of the variables includes \( p^0 \) (which is \( 1 \)) and \( q^0 \) (which is \( 1 \)) since no variable is present in all three monomials.

Thus, the GCF of \( 65p^2 \), \( 26pq \), and \( 39q^2 \) is:

\[
\text{GCF} = 13
\]

So the GCF of the monomials \( 65p^2 \), \( 26pq \), and \( 39q^2 \) is **13**.