Every positive composite number only has one unique prime factorization.
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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.
120 has the prime factorization 8 x 3 x 5
120 = 2x2x2x3x5 = 23x31x51
120 = 23 x 31 x 51
23 x 3 x 5 = 120