1. **State the problem:** Find the greatest common factor (GCF) of the terms $91x$ and $143$. 2. **Prime factorization:** - Factor $91x$ into prime factors: $91 = 7 \times 13$, so $91x = 7 \times 13 \times x$. - Factor $143$ into prime factors: $143 = 11 \times 13$. 3. **Identify common factors:** - Both terms share the factor $13$. - $x$ is only in $91x$, and $7$ and $11$ are unique to each term. 4. **Conclusion:** - The GCF is the product of the common prime factors, which is $13$. **Final answer:** The GCF of $91x$ and $143$ is $13$.