Kelley May
10/10/2023 · Junior High School
Find the greatest common factor of 49 and 18.
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To find the greatest common factor (GCF) of 49 and 18, we can use the prime factorization method.
1. **Prime factorization of 49**:
- 49 can be expressed as \(7 \times 7\) or \(7^2\).
2. **Prime factorization of 18**:
- 18 can be expressed as \(2 \times 3 \times 3\) or \(2 \times 3^2\).
3. **List the prime factors**:
- The prime factors of 49 are \(7\).
- The prime factors of 18 are \(2\) and \(3\).
4. **Identify common factors**:
- The only prime factor of 49 is \(7\), and the prime factors of 18 are \(2\) and \(3\). There are no common prime factors between 49 and 18.
Since there are no common factors, the greatest common factor (GCF) of 49 and 18 is:
\[
\text{GCF} = 1
\]
Thus, the greatest common factor of 49 and 18 is \(1\).
Quick Answer
The greatest common factor of 49 and 18 is 1.
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