`(289)/(391)` when reduced to lowest term is .

Options

A. `(13)/(17)`
B. `(17)/(19)`
C. `(17)/(23)`
D. `(17)/(21)`

Answer

To reduce the fraction \( \frac{289}{391} \) to its lowest terms, we need to find the greatest common divisor (GCD) of the numerator (289) and the denominator (391) and then divide both by that GCD.

### Step-by-Step Solution:

1. **Find the GCD of 289 and 391:**
- To find the GCD, we can use the prime factorization method or the Euclidean algorithm. Here, we will check for common factors.
- First, we can check if 289 is divisible by any small prime numbers. We find that \( 289 = 17 \times 17 \) (or \( 17^2 \)).
- Next, we check 391. We can divide 391 by 17:
\[ 391 \div 17 = 23 \]
- So, \( 391 = 17 \times 23 \).

2. **Identify the common factor:**
- The common factor between 289 and 391 is 17.

3. **Divide both the numerator and the denominator by the GCD (17):**
- Now we divide both 289 and 391 by 17:
\[ \frac{289 \div 17}{391 \div 17} = \frac{17}{23} \]

4. **Conclusion:**
- The fraction \( \frac{289}{391} \) when reduced to its lowest terms is \( \frac{17}{23} \).

### Final Answer:
\[ \frac{289}{391} = \frac{17}{23} \]