1. The problem is to simplify the given fractions by finding their Greatest Common Factor (GCF) and then dividing numerator and denominator by the GCF. 2. The formula to simplify a fraction $\frac{a}{b}$ is: $$\frac{a}{b} = \frac{a \div \text{GCF}(a,b)}{b \div \text{GCF}(a,b)}$$ where GCF is the greatest common factor of $a$ and $b$. 3. Let's find the factors, common factors (CF), GCF, and simplified solution for each fraction: - For $\frac{8}{72}$: - Factors of 8: 1, 2, 4, 8 - Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 - Common factors: 1, 2, 4, 8 - GCF: 8 - Simplified fraction: $\frac{8 \div 8}{72 \div 8} = \frac{1}{9}$ - For $\frac{15}{25}$: - Factors of 15: 1, 3, 5, 15 - Factors of 25: 1, 5, 25 - Common factors: 1, 5 - GCF: 5 - Simplified fraction: $\frac{15 \div 5}{25 \div 5} = \frac{3}{5}$ - For $\frac{24}{36}$: - Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 - Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 - Common factors: 1, 2, 3, 4, 6, 12 - GCF: 12 - Simplified fraction: $\frac{24 \div 12}{36 \div 12} = \frac{2}{3}$ - For $\frac{40}{60}$: - Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40 - Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 - Common factors: 1, 2, 4, 5, 10, 20 - GCF: 20 - Simplified fraction: $\frac{40 \div 20}{60 \div 20} = \frac{2}{3}$ - For $\frac{35}{49}$: - Factors of 35: 1, 5, 7, 35 - Factors of 49: 1, 7, 49 - Common factors: 1, 7 - GCF: 7 - Simplified fraction: $\frac{35 \div 7}{49 \div 7} = \frac{5}{7}$ 4. Summary of solutions: - $\frac{8}{72} = \frac{1}{9}$ - $\frac{15}{25} = \frac{3}{5}$ - $\frac{24}{36} = \frac{2}{3}$ - $\frac{40}{60} = \frac{2}{3}$ - $\frac{35}{49} = \frac{5}{7}$ This method ensures fractions are simplified to their lowest terms by dividing numerator and denominator by their greatest common factor.