Use divisibility rules, prime factorization, and factor structure to analyze and solve whole-number problems.
Combine divisibility clues and factor structure
Problem
Identify every number in this list that divides \(360\) evenly: \(8\), \(9\), \(10\), \(12\), \(14\), \(15\), \(18\), \(24\), \(45\).
Big Picture
What this problem is really about
Testing nine possible divisors one by one is clearer if we first expose the prime structure of three hundred sixty. We’ll factor the target number, compare each listed number’s prime factors with what is available, and use whole-number quotients as checks. A number fails as soon as it requires a missing prime or a higher exponent.
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