10 to the power of 2 is common to all these numbers. Not the answer that I am looking for...
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How about this:
All are evenly divisible by nine. Also, 225 is a perfect square (15), 216 is a perfect cube (6), and the others are prime multiples of nine... but these features are not common to the lot.
There are 17 numbers between 150 and 300 that are divisible by nine: 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297.
6 squared = 36 6 cubed = 216 3 cubed = 27 36 + 216 - 27 = 225
32 + 63 = 9 + 216 = 225
Least Common Multiple (LCM) for 15 75 45 is 225.
The LCM is: 2,250
All the numbers are divisible by: 9
99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, . . .
90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, . . .
There are 17 numbers between 150 and 300 that are divisible by nine: 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297.
The GCF is 9.
9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270
92%
There are 33 such numbers: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297.
Enter these into a calculator and you will have your answer: 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396.
189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, . . . (infinite)
6 squared = 36 6 cubed = 216 3 cubed = 27 36 + 216 - 27 = 225
9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351 and keep adding nine until you get to 999.