Use divisibility rules, prime factorization, and factor structure to analyze and solve whole-number problems.
Translate a structure representation into standard form
Problem
A factor tree shows \(90\) splitting into \(9\) and \(10\), then into \(3\), \(3\), \(2\), and \(5\). Write the prime factorization represented by the tree.
The information we need sits at the ends of the factor tree, not at its first split. We’ll follow both composite branches until the leaves are prime, collect every leaf, group repeated primes with an exponent, and multiply the result back to ninety. That prevents us from stopping at a partial factorization.
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