Question

Identify the greatest common factor of 50, c, x50cx and 37, c37c.

Answer 1

To find the greatest common factor (GCF) of the terms \(50\), \(c\), \(50cx\), and \(37c\), let's break down each component:

1. **Numerical Coefficients**:
- The numbers involved are \(50\) and \(37\).
- The prime factorization of \(50\) is \(2 \times 5^2\).
- The prime factorization of \(37\) is just \(37\) (since \(37\) is a prime number).

Since \(50\) and \(37\) have no common prime factors, their GCF is \(1\).

2. **Variables**:
- The variables involved are \(c\), \(50cx\), and \(37c\).
- The common variable among these terms is \(c\).
- The term \(c\) appears explicitly, while \(50cx\) and \(37c\) both contain \(c\) as well.

Next, we combine the results:
- The GCF of the numerical coefficients is \(1\).
- The GCF of the variable part is \(c\).

Thus, when combining these results, the overall GCF of \(50\), \(c\), \(50cx\), and \(37c\) is:

\[
\text{GCF} = 1 \cdot c = c
\]

Therefore, the greatest common factor of \(50\), \(c\), \(50cx\), and \(37c\) is:

\[
\boxed{c}
\]