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The common factors of 288 and 420 are 1, 2, 3, 4, 6 and 12.
3 is the only common factor.
30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, ...
360, 420 and 480 all have 24 factors.
Prime factorization of 270: 2x3x3x3x5 So any one of these factors or combination of these factors will divide exactly into 270. Any number that is not one of these factors or a combination will not. For example, 3x3x3x2=54 so 54 will divide exactly into 270. 270/54 = 5