768 = 28 x 31
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Using prime factorization, there are 2 three digit numbers with 9 factors: 512 and 768. There are no three digit numbers with 10 or more prime factors. 512=2^9 and 768=3*2^8
The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, and 768. The prime factors of 768 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3.
512 = 29 or 768 = 28*3 have 9 prime factors each.
16*48
48 gallons is 768 cups.