Use divisibility rules, prime factorization, and factor structure to analyze and solve whole-number problems.
Check a prime-structure claim
Problem
A student says \(8~\times~9\) is the complete prime factorization of \(72\). Is the claim correct? If not, what is the corrected prime factorization?
Big Picture
What this problem is really about
A correct product is not automatically a complete prime factorization. We’ll verify that eight times nine gives seventy-two, check whether each displayed factor is prime, and continue decomposing any composite factor until only primes remain. Then we’ll compress repeats with exponents and multiply back to confirm the corrected structure.
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