Reduce each of the following fractions to the lowest terms :
(i) `(161)/(207)` , (ii) `(517)/(799)` , (iii) `(296)/(481)`

Answer

To reduce each of the given fractions to their lowest terms, we will follow these steps:

### Step 1: Reduce the fraction \( \frac{161}{207} \)

1. **Find the GCD (Greatest Common Divisor)** of 161 and 207.
- The prime factorization of 161 is \( 7 \times 23 \).
- The prime factorization of 207 is \( 9 \times 23 \) (or \( 3^2 \times 23 \)).
- The common factor is \( 23 \).

2. **Divide both the numerator and denominator by their GCD**:
\[ \frac{161 \div 23}{207 \div 23} = \frac{7}{9} \]

### Step 2: Reduce the fraction \( \frac{517}{799} \)

1. **Find the GCD of 517 and 799**.
- The prime factorization of 517 is \( 47 \times 11 \).
- The prime factorization of 799 is \( 47 \times 17 \).
- The common factor is \( 47 \).

2. **Divide both the numerator and denominator by their GCD**:
\[ \frac{517 \div 47}{799 \div 47} = \frac{11}{17} \]

### Step 3: Reduce the fraction \( \frac{296}{481} \)

1. **Find the GCD of 296 and 481**.
- The prime factorization of 296 is \( 37 \times 8 \) (or \( 37 \times 2^3 \)).
- The prime factorization of 481 is \( 37 \times 13 \).
- The common factor is \( 37 \).

2. **Divide both the numerator and denominator by their GCD**:
\[ \frac{296 \div 37}{481 \div 37} = \frac{8}{13} \]

### Final Answers:
- (i) \( \frac{161}{207} = \frac{7}{9} \)
- (ii) \( \frac{517}{799} = \frac{11}{17} \)
- (iii) \( \frac{296}{481} = \frac{8}{13} \)

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