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

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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:

\[ \boxed{c} \]