24. Find GCF \( (180,300) \).

To find the greatest common factor (GCF) of 180 and 300, we'll start by expressing each number as a product of its prime factors. Step 1: Prime Factorization • For 180:   180 = 2 × 90      = 2 × (2 × 45)      = 2² × 45      = 2² × (3 × 15)      = 2² × 3 × (3 × 5)      = 2² × 3² × 5 • For 300:   300 = 2 × 150      = 2 × (2 × 75)      = 2² × 75      = 2² × (3 × 25)      = 2² × 3 × (5 × 5)      = 2² × 3 × 5² Step 2: Determine the GCF The GCF is found by taking the product of the common prime factors with the smallest exponents. - For the prime 2: Both numbers have 2². - For the prime 3: 180 has 3² and 300 has 3¹, so we take 3¹. - For the prime 5: 180 has 5¹ and 300 has 5², so we take 5¹. Now, multiply these together:   GCF = 2² × 3¹ × 5¹ = 4 × 3 × 5 = 60 Thus, the greatest common factor of 180 and 300 is 60.