561744000 has 384 divisors, whose sum is σ = 2085108480. Its totient is φ = 144844800.

The previous prime is 561743999. The next prime is 561744011. The reversal of 561744000 is 447165.

561744000 = 270³ + 271³ + ... + 294³.

561744000 is a `hidden beast` number, since 5 + 617 + 4 + 40 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (384).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 6767959 + ... + 6768041.

It is an arithmetic number, because the mean of its divisors is an integer number (5429970).

Almost surely, 2^561744000 is an apocalyptic number.

561744000 is a gapful number since it is divisible by the number (50) 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 561744000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1042554240).

561744000 is an abundant number, since it is smaller than the sum of its proper divisors (1523364480).

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

561744000 is a wasteful number, since it uses less digits than its factorization.

561744000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 165 (or 140 counting only the distinct ones).

The product of its (nonzero) digits is 3360, while the sum is 27.

The square root of 561744000 is about 23701.1392131264. The cubic root of 561744000 is about 825.1118305705. Note that the first 3 decimals are identical.

The spelling of 561744000 in words is "five hundred sixty-one million, seven hundred forty-four thousand".