1. **Problem:** Simplify the fraction $\frac{8}{24}$.\n - Factors of numerator: $8 = 2 \times 2 \times 2$.\n - Factors of denominator: $24 = 2 \times 2 \times 2 \times 3$.\n - Common factors: $2 \times 2 \times 2 = 8$.\n - GCF = 8.\n - Simplified fraction: $\frac{8 \div 8}{24 \div 8} = \frac{1}{3}$.\n\n2. **Problem:** Simplify the fraction $\frac{4}{28}$.\n - Factors of numerator: $4 = 2 \times 2$.\n - Factors of denominator: $28 = 2 \times 2 \times 7$.\n - Common factors: $2 \times 2 = 4$.\n - GCF = 4.\n - Simplified fraction: $\frac{4 \div 4}{28 \div 4} = \frac{1}{7}$.\n\n3. **Problem:** Simplify the fraction $\frac{6}{30}$.\n - Factors of numerator: $6 = 2 \times 3$.\n - Factors of denominator: $30 = 2 \times 3 \times 5$.\n - Common factors: $2 \times 3 = 6$.\n - GCF = 6.\n - Simplified fraction: $\frac{6 \div 6}{30 \div 6} = \frac{1}{5}$.\n\n4. **Problem:** Simplify the fraction $\frac{30}{20}$.\n - Factors of numerator: $30 = 2 \times 3 \times 5$.\n - Factors of denominator: $20 = 2 \times 2 \times 5$.\n - Common factors: $2 \times 5 = 10$.\n - GCF = 10.\n - Simplified fraction: $\frac{30 \div 10}{20 \div 10} = \frac{3}{2}$.\n\n5. **Problem:** Simplify the mixed number $2 \frac{12}{36}$.\n - Convert to improper fraction: $2 \frac{12}{36} = \frac{2 \times 36 + 12}{36} = \frac{72 + 12}{36} = \frac{84}{36}$.\n - Factors of numerator: $84 = 2 \times 2 \times 3 \times 7$.\n - Factors of denominator: $36 = 2 \times 2 \times 3 \times 3$.\n - Common factors: $2 \times 2 \times 3 = 12$.\n - GCF = 12.\n - Simplified fraction: $\frac{84 \div 12}{36 \div 12} = \frac{7}{3}$.\n - Convert back to mixed number: $\frac{7}{3} = 2 \frac{1}{3}$.