Use divisibility rules, prime factorization, and factor structure to analyze and solve whole-number problems.
Use prime factor structure for specified numeric outputs
Problem
Find the prime factorization of \(72\) and calculate the number of tiles per row in \(8\) equal rows.
Big Picture
What this problem is really about
The two requested results come from the same factor pair. We’ll split seventy-two into eight times the unknown row length, decompose both factors completely into primes, and count repeated primes with exponents. The quotient by eight gives the tiles per row, while multiplying the prime powers back checks the factorization.
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