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only using the numbers once
The prime factorization of 120 is not 2345 because 2345 is not a factor of 120. The prime factorization of 120 is 2^3 * 3 * 5, which means that 120 can be expressed as the product of primes 2, 3, and 5.
Assuming all of {7, 8, 2, 3} have to be used exactly once: (8 - 2) x (7 - 3) = 24.
24
3! = 6.