1. The problem is to find the Greatest Common Factor (GCF) of 36 and 72. 2. The GCF of two numbers is the largest number that divides both of them without leaving a remainder. 3. To find the GCF, we can use the prime factorization method: 4. Prime factorize 36: $$36 = 2^2 \times 3^2$$ 5. Prime factorize 72: $$72 = 2^3 \times 3^2$$ 6. Identify the common prime factors with the smallest powers: - For 2, the smallest power is $2^2$ - For 3, the smallest power is $3^2$ 7. Multiply these common factors: $$GCF = 2^2 \times 3^2 = 4 \times 9 = 36$$ 8. Therefore, the GCF of 36 and 72 is 36.