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Identify the greatest common factor of 22, w22w and 33, a, cubed, w33a
3
w.
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Identify the greatest common factor of 22, w22w and 33, a, cubed, w33a
3
w.
Answer
Attempt 1 out of 5
Answers
GPT-4o mini
To find the greatest common factor (GCF) of the numbers and expressions provided, we first need to identify each component clearly.
1. **Identify the components:**
- **22**: This is a straightforward integer.
- **w22w**: This expression seems to involve a variable 'w' and appears to be a product that includes 22 as a coefficient and possibly two occurrences of 'w'.
- **33**: This is another integer.
- **a³w33a**: This involves a variable 'a', indicating 'a' is raised to the third power and includes a coefficient of 33 and possibly another occurrence of 'a'.
2. **Break down the factors:**
- **22** factors to \( 2 \times 11 \).
- **w22w**: Since 'w' is not a numerical factor but rather a variable, we can write it as \( 22w^2 \) if we assume 'w' appears twice.
- **33** factors to \( 3 \times 11 \).
- **a³w33a**: Similarly, we can consider this as \( 33a^4 \) if there are two occurrences of 'a' multiplying \( a^3 \).
3. **List the factors for GCF:**
- For **numbers only (22 and 33)**:
- Factors of 22: \( 1, 2, 11, 22 \)
- Factors of 33: \( 1, 3, 11, 33 \)
- The common factor is **11**.
4. **Include variables**:
- Both \( w22w \) and \( a³w33a \) include the variables \( w \) and \( a \).
- The GCF will involve the lowest powers of these variables that exist in both expressions.
- Here, \( w^2 \) and \( a^4 \) do not have common terms, so we can't include them in the GCF.
5. **Conclusion**:
- The GCF of the numerical coefficients (22 and 33) is **11**.
- For the expressions, if we strictly consider the numerical part, the GCF remains **11**.
- Since there's no common \( a \) or \( w \), the GCF of both numerical expressions is **11**.
Thus, the **greatest common factor (GCF)** of \( 22, w22w, 33, \) and \( a³w33a \) is **11**.
1. **Identify the components:**
- **22**: This is a straightforward integer.
- **w22w**: This expression seems to involve a variable 'w' and appears to be a product that includes 22 as a coefficient and possibly two occurrences of 'w'.
- **33**: This is another integer.
- **a³w33a**: This involves a variable 'a', indicating 'a' is raised to the third power and includes a coefficient of 33 and possibly another occurrence of 'a'.
2. **Break down the factors:**
- **22** factors to \( 2 \times 11 \).
- **w22w**: Since 'w' is not a numerical factor but rather a variable, we can write it as \( 22w^2 \) if we assume 'w' appears twice.
- **33** factors to \( 3 \times 11 \).
- **a³w33a**: Similarly, we can consider this as \( 33a^4 \) if there are two occurrences of 'a' multiplying \( a^3 \).
3. **List the factors for GCF:**
- For **numbers only (22 and 33)**:
- Factors of 22: \( 1, 2, 11, 22 \)
- Factors of 33: \( 1, 3, 11, 33 \)
- The common factor is **11**.
4. **Include variables**:
- Both \( w22w \) and \( a³w33a \) include the variables \( w \) and \( a \).
- The GCF will involve the lowest powers of these variables that exist in both expressions.
- Here, \( w^2 \) and \( a^4 \) do not have common terms, so we can't include them in the GCF.
5. **Conclusion**:
- The GCF of the numerical coefficients (22 and 33) is **11**.
- For the expressions, if we strictly consider the numerical part, the GCF remains **11**.
- Since there's no common \( a \) or \( w \), the GCF of both numerical expressions is **11**.
Thus, the **greatest common factor (GCF)** of \( 22, w22w, 33, \) and \( a³w33a \) is **11**.