Question
Identify the greatest common factor of 49bz and 21bx
Answers
Answered by
GPT-4o mini
To find the greatest common factor (GCF) of the terms \(49bz\) and \(21bx\), we can start by breaking down each term into its factors.
1. **Factor the coefficients:**
- The coefficients are \(49\) and \(21\).
- The prime factorization of \(49\) is \(7^2\).
- The prime factorization of \(21\) is \(3 \times 7\).
2. **Find the GCF of the coefficients:**
- The common prime factor is \(7\).
- The lowest power of \(7\) common to both factorizations is \(7^1\).
- Therefore, the GCF of \(49\) and \(21\) is \(7\).
3. **Factor the variables:**
- The variable \(b\) is present in both terms as \(bz\) and \(bx\).
- The GCF of \(b\) is simply \(b\) since it is present in both.
4. **Combine the GCF of the coefficients and variables:**
- The GCF of \(49bz\) and \(21bx\) is \(7b\).
Therefore, the greatest common factor of \(49bz\) and \(21bx\) is \( \boxed{7b} \).
1. **Factor the coefficients:**
- The coefficients are \(49\) and \(21\).
- The prime factorization of \(49\) is \(7^2\).
- The prime factorization of \(21\) is \(3 \times 7\).
2. **Find the GCF of the coefficients:**
- The common prime factor is \(7\).
- The lowest power of \(7\) common to both factorizations is \(7^1\).
- Therefore, the GCF of \(49\) and \(21\) is \(7\).
3. **Factor the variables:**
- The variable \(b\) is present in both terms as \(bz\) and \(bx\).
- The GCF of \(b\) is simply \(b\) since it is present in both.
4. **Combine the GCF of the coefficients and variables:**
- The GCF of \(49bz\) and \(21bx\) is \(7b\).
Therefore, the greatest common factor of \(49bz\) and \(21bx\) is \( \boxed{7b} \).
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