The following puzzle was put on the board. We are two natural numbers. Our difference is 30, and our greatest common factor is 15, and our sum is 120. Who are we? 15 and 30, since our greatest common divisor is 15. 15 and 45, since our difference is 30 and our greatest common factor is 15. 15 and 105, since our sum is 120 and our greatest common factor is 15.

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