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The greatest common factor of 144 and 175 is 1.
Factoring completely, we determine:
144 = 12 * 12 = 3 * 3 * 4 * 4 = 3 * 3 * 2 * 2 * 2 * 2 * 1
175 = 7 * 25 = 7 * 5 * 5 * 1
Since the only factor these have in common is 1, 1 is their greatest common factor.
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