which has a gcf of 5m^2n^2
m^5n^3

5m^4n^3

10m^4n

15m^2n^2

24m^3n^4

To find which pair of terms has the greatest common factor (GCF) of \( 5m^2n^2 \), we can follow these steps:

1. **Factorize each term completely**:
   - \( m^5n^3 \): The factors are \( m^5 \times n^3 \).
   - \( 5m^4n^3 \): The factors are \( 5 \times m^4 \times n^3 \).
   - \( 10m^4n \): The factors are \( 2 \times 5 \times m^4 \times n \).
   - \( 15m^2n^2 \): The factors are \( 3 \times 5 \times m^2 \times n^2 \).
   - \( 24m^3n^4 \): The factors are \( 2^3 \times 3 \times m^3 \times n^4 \).

2. **Identify the GCF for each pair**:
   - **\( m^5n^3 \) and \( 5m^4n^3 \)**:
     - GCF = \( m^4n^3 \).
   - **\( m^5n^3 \) and \( 10m^4n \)**:
     - GCF = \( 5m^4n \).
   - **\( m^5n^3 \) and \( 15m^2n^2 \)**:
     - GCF = \( 5m^2n^2 \).
   - **\( m^5n^3 \) and \( 24m^3n^4 \)**:
     - GCF = \( m^3n^3 \).
   - **\( 5m^4n^3 \) and \( 10m^4n \)**:
     - GCF = \( 5m^4n \).
   - **\( 5m^4n^3 \) and \( 15m^2n^2 \)**:
     - GCF = \( 5m^2n^2 \).
   - **\( 5m^4n^3 \) and \( 24m^3n^4 \)**:
     - GCF = \( m^3n^3 \).
   - **\( 10m^4n \) and \( 15m^2n^2 \)**:
     - GCF = \( 5m^2n \).
   - **\( 10m^4n \) and \( 24m^3n^4 \)**:
     - GCF = \( 2m^3n \).
   - **\( 15m^2n^2 \) and \( 24m^3n^4 \)**:
     - GCF = \( m^2n^2 \).

From the analysis above, the following pairs have a GCF of \( 5m^2n^2 \):
1. \( m^5n^3 \) and \( 15m^2n^2 \)
2. \( 5m^4n^3 \) and \( 15m^2n^2 \)

So, the terms that have a GCF of \( 5m^2n^2 \) are:

- **\( m^5n^3 \) and \( 15m^2n^2 \)**
- **\( 5m^4n^3 \) and \( 15m^2n^2 \)**

Would you like more details on how to find the GCF or any other aspect of this problem?

Here are 5 related questions for further practice:
1. What is the GCF of \( 12x^3y^2 \) and \( 18x^2y^3 \)?
2. How do you factorize \( 5m^4n^3 \) completely?
3. What is the GCF of \( 8a^2b^3c \) and \( 12a^3b^2c^2 \)?
4. How do you find the GCF of three or more algebraic expressions?
5. What is the GCF of \( 21m^5n^2 \) and \( 14m^3n^4 \)?

**Tip:** Always factorize the terms completely before finding the GCF. This makes it easier to compare the factors and identify the common ones.

Learn how to find the Greatest Common Factor (GCF) of algebraic expressions with practice problems. This page covers detailed steps to identify the GCF, including factorization and comparison of terms. Suitable for students in Grades 7-9.

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