Question
How many even divisors does 360 have?
Solution
Prime factorization: 360 = 2³ × 3² × 5¹ Total number of divisors = (3 + 1)(2 + 1)(1 + 1) = 4 × 3 × 2 = 24 Odd divisors are formed without factor 2: Odd part = 3² × 5¹ Number of odd divisors = (2 + 1)(1 + 1) = 3 × 2 = 6 Even divisors = Total divisors − Odd divisors = 24 − 6 = 18 Answer: 18 even divisors
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