Use divisibility rules, prime factorization, and factor structure to analyze and solve whole-number problems.
Choose a specified whole-number structure tool
Problem
Which is more efficient for testing whether \(8,190\) is divisible by \(2,~3,~5,~6,~9,~\text{and}~10\): divisibility rules or full prime factorization? Name the method, then identify every divisor from the list.
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What this problem is really about
The requested divisors all have quick tests, so full prime factorization would add work without helping. We’ll use the last digit of eight thousand one hundred ninety to test two, five, and ten, use its digit sum to test three and nine, and combine the two-and-three results for six. Whole-number quotients can verify the final set.
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