Question

Find the GCF of the monomials 55 p squared​, 33​pq, and 22 q squared.
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Part 1
The GCF of 55 p squared​, 33​pq, and 22 q squared is

Answer 1

To find the GCF (greatest common factor) of the monomials \(55p^2\), \(33pq\), and \(22q^2\), we will need to find the GCF of the coefficients and the GCF of the variables separately.

1. **Coefficients**:
- The coefficients are \(55\), \(33\), and \(22\).
- To find the GCF of these numbers, we can factor each one:
- \(55 = 5 \times 11\)
- \(33 = 3 \times 11\)
- \(22 = 2 \times 11\)
- The only common factor among \(55\), \(33\), and \(22\) is \(11\).

2. **Variables**:
- For the variables:
- \(55p^2\) has \(p^2\)
- \(33pq\) has \(p^1q^1\)
- \(22q^2\) has \(q^2\)
- The GCF for \(p\) is \(p^{\min(2, 1, 0)} = p^0 = 1\) (as \(22q^2\) contains no \(p\)).
- The GCF for \(q\) is \(q^{\min(0, 1, 2)} = q^0 = 1\) (as \(55p^2\) contains no \(q\)).

Putting it all together:
- The GCF of the coefficients is \(11\).
- The GCF of the variables is \(1\).

Therefore, the GCF of the monomials \(55p^2\), \(33pq\), and \(22q^2\) is:

\[
\text{GCF} = 11
\]