By how many positive integers less than 10 is 27²⁷ – 9⁴⁰ – 3⁷⁹ divisible?

Express as powers of 3: 27²⁷ = 3⁸¹, 9⁴⁰ = 3⁸⁰, 3⁷⁹ = 3⁷⁹. So expression = 3⁸¹ – 3⁸⁰ – 3⁷⁹ = 3⁷⁹(3² – 3 – 1) = 3⁷⁹ × 5. The positive integers less than 10 dividing 3⁷⁹ × 5 are: 1, 3, 5, 9 (3² divides 3⁷⁹). That's 4 divisors, which is more than 3.