Math CentralQuandaries & Queries


Question from Lorraine, a student:

What is the smallest possible sum that can be obtained by adding five positive integers that have a product of 48.


First make a list of all the the positive integers that divide evenly into 48 -- there is 1 and 48, 2 and 24, 3 and 16, and so on. (Your list should contain 10 numbers.) Then add up 4 ones and 48. Then add up 3 ones and the pairs whose product is 48 (such as 2 and 24). Next add 2 ones and all possible triples that equal 48 (such as 2, 2, and 12). Then 1 one and quadruples whose product is 48 (such as 2, 2, 2, and 6). Finally add up 2, 2, 2, 2, and 3. Which sum is smallest?


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