Find factors, multiples, common factors, and common multiples to solve numerical and contextual problems.
Use factors for equal-group arrangements
Problem
A teacher has \(24\) desks to arrange in equal rows for a class photo. List all possible rectangular arrangements of the desks. Do not count turning the same arrangement sideways as a different one.
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What this problem is really about
Every rectangular desk arrangement corresponds to a factor pair whose product is twenty-four. We’ll test row counts in order, pair each divisor with the number of desks per row, and stop when reversing the factors would only turn a rectangle sideways. This gives a complete set without counting the same shape twice.
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