ExplanationSince a prime number has only two factors, 1 and itself, \((2^a)(3^b)(5^c)\) cannot be prime unless the digits a, b, and c are such that two of the digits are 0 and the third is 1.
For instance, \((2^0)(3^1)(5^0) = (1)(3)(1) = 3\) is prime.
Thus, the only three values of abc that would result in a prime number & (abc)& are 100, 010, and 001. However, only one of those three numbers (100) is a three-digit number.
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