Use divisibility rules, prime factorization, and factor structure to analyze and solve whole-number problems.
Apply a named whole-number structure conclusion
Problem
A whole number's digits add to \(27\). Must the number be divisible by \(9\)?
Big Picture
What this problem is really about
The phrase “digits add to twenty-seven” points directly to the divisibility rule for nine. We’ll test whether the given digit sum is a multiple of nine and transfer that remainder result to the unknown whole number. The actual digits are unnecessary because every number has the same remainder modulo nine as its digit sum.
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