205664400 has 240 divisors, whose sum is σ = 742660800. Its totient is φ = 54051840.

The previous prime is 205664387. The next prime is 205664411. The reversal of 205664400 is 4466502.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (240).

It is a super-3 number, since 3×205664400³ (a number of 26 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1479531 + ... + 1479669.

It is an arithmetic number, because the mean of its divisors is an integer number (3094420).

Almost surely, 2^205664400 is an apocalyptic number.

205664400 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 205664400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (371330400).

205664400 is an abundant number, since it is smaller than the sum of its proper divisors (536996400).

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

205664400 is a wasteful number, since it uses less digits than its factorization.

205664400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 303 (or 286 counting only the distinct ones).

The product of its (nonzero) digits is 5760, while the sum is 27.

The square root of 205664400 is about 14341.0041489430. The cubic root of 205664400 is about 590.2731666209.

The spelling of 205664400 in words is "two hundred five million, six hundred sixty-four thousand, four hundred".