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An interesting aspect of fractions and prime factorization is that multiplying fractions is the same as adding the prime numerators and subtracting the prime denominators.
For example, multiplying 42 by 5/14 means incrementing the power of prime 5, and decrementing the power of primes 2 and 7 — For a result of 42. A division is simply the inversion of the effects of the numerator and denumerator.
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