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The best way to have many factors is to build a number by multiplying many small numbers together. For example, a number that is the product of 2x3x4x5 will have many factors. 2x3x4x5 is 120. The factors of 120 are (listed as factor pairs) 1,120, 2,60, 3,40, 4,30, 5,24, 6,20, 8,15, 10,12. That's 16 factors.

How about if we multiplied out 2's and 3's until the number was just below 150: 2x3x2x3x2 is 72. We can't get away with another 3 so put in another 2: 2x3x2x3x2x2 is 144. The factors of 144 are 1,144, 2,72, 3,48, 4,36, 6,24, 8,18, 9,16, 12,12. That is also 16 factors, but we can't really count 12 twice, so there are only 15 unique factors of 144.

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12y ago

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