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A certain integer has only two distinct prime factors. The number of its divisors is 6, and the sum of the divisors is 28. The integer is_______
Correct Answer: 12
With two distinct primes and 6 divisors, the number is $$p^2 q$$, and the divisor sum is $$(1 + p + p^2)(1 + q) = 28$$. The only factorisation that works is $$7 \times 4$$, giving $$p = 2$$ and $$q = 3$$. The integer is $$2^2 \times 3 = 12$$ (divisors 1, 2, 3, 4, 6, 12, sum 28).
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