1. Stating the problem: Find the greatest common divisor (GCD) of the given numbers. 2. Formula and rules: The GCD of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder. 3. For part (a), find GCD of 130 and 195: - Prime factorization of 130: $$130 = 2 \times 5 \times 13$$ - Prime factorization of 195: $$195 = 3 \times 5 \times 13$$ - Common prime factors: 5 and 13 - Multiply common factors: $$5 \times 13 = 65$$ - So, GCD(130, 195) = 65 4. For part (b), find GCD of 180, 216, and 288: - Prime factorization of 180: $$180 = 2^2 \times 3^2 \times 5$$ - Prime factorization of 216: $$216 = 2^3 \times 3^3$$ - Prime factorization of 288: $$288 = 2^5 \times 3^2$$ - Common prime factors with minimum powers: - For 2: minimum power is 2 - For 3: minimum power is 2 - For 5: not common to all three - Multiply common factors with minimum powers: $$2^2 \times 3^2 = 4 \times 9 = 36$$ - So, GCD(180, 216, 288) = 36 Final answers: - a. 65 - b. 36