205920 has 144 divisors (see below), whose sum is σ = 825552. Its totient is φ = 46080.

The previous prime is 205913. The next prime is 205937. The reversal of 205920 is 29502.

It is a tau number, because it is divible by the number of its divisors (144).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a junction number, because it is equal to n+sod(n) for n = 205893 and 205902.

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 205920.

It is an unprimeable number.

205920 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 15834 + ... + 15846.

It is an arithmetic number, because the mean of its divisors is an integer number (5733).

2²⁰⁵⁹²⁰ is an apocalyptic number.

205920 is a gapful number since it is divisible by the number (20) 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 205920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (412776).

205920 is an abundant number, since it is smaller than the sum of its proper divisors (619632).

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

205920 is a wasteful number, since it uses less digits than its factorization.

205920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 45 (or 34 counting only the distinct ones).

The product of its (nonzero) digits is 180, while the sum is 18.

The square root of 205920 is about 453.7840896285. The cubic root of 205920 is about 59.0517596158.

The spelling of 205920 in words is "two hundred five thousand, nine hundred twenty".