Problem preview
MF.NS.6 Challenge MF-006-A12-V01

Use divisibility rules, prime factorization, and factor structure to analyze and solve whole-number problems.

Filter candidates by number-structure conditions

Problem

Determine the number that is divisible by \(6\), not divisible by \(9\), and composite.

Big Picture

What this problem is really about

We can handle the three conditions as filters instead of testing everything at once. We’ll first keep numbers divisible by six, use digit sums to remove those divisible by nine, and then verify that the remaining value has a nontrivial factor pair. Passing an early filter does not excuse failing a later one.

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Four variants of this problem type
Curriculum context
Standard
MF.NS.6
Category
Number Sense
Domain
Whole-Number Structure
Objective
Use divisibility rules, prime factorization, and factor structure to analyze and solve whole-number problems.
Problem type
Filter candidates by number-structure conditions