345984 has 64 divisors (see below), whose sum is σ = 991440. Its totient is φ = 106496.

The previous prime is 345979. The next prime is 345997. The reversal of 345984 is 489543.

345984 = T₁₈₇ + T₁₈₈ + ... + T₂₀₄.

345984 is nontrivially palindromic in base 7.

It is a tau number, because it is divible by the number of its divisors (64).

It is a Smith number, since the sum of its digits (33) coincides with the sum of the digits of its prime factors.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 345984.

It is an unprimeable number.

345984 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 6502 + ... + 6554.

2³⁴⁵⁹⁸⁴ is an apocalyptic number.

345984 is a gapful number since it is divisible by the number (34) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 345984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (495720).

345984 is an abundant number, since it is smaller than the sum of its proper divisors (645456).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

345984 is a wasteful number, since it uses less digits than its factorization.

345984 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 87 (or 75 counting only the distinct ones).

The product of its digits is 17280, while the sum is 33.

The square root of 345984 is about 588.2040462289. The cubic root of 345984 is about 70.2024073654.

The spelling of 345984 in words is "three hundred forty-five thousand, nine hundred eighty-four".