561398400 has 288 divisors, whose sum is σ = 2033513820. Its totient is φ = 147456000.

The previous prime is 561398359. The next prime is 561398401. The reversal of 561398400 is 4893165.

561398400 is a `hidden beast` number, since 561 + 3 + 98 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 289544256 + 271854144 = 17016^2 + 16488^2 .

It is a tau number, because it is divible by the number of its divisors (288).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (561398401) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 2908704 + ... + 2908896.

Almost surely, 2^561398400 is an apocalyptic number.

561398400 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 561398400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1016756910).

561398400 is an abundant number, since it is smaller than the sum of its proper divisors (1472115420).

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

561398400 is a wasteful number, since it uses less digits than its factorization.

561398400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 324 (or 304 counting only the distinct ones).

The product of its (nonzero) digits is 25920, while the sum is 36.

The square root of 561398400 is about 23693.8473026227. The cubic root of 561398400 is about 824.9425855361.

The spelling of 561398400 in words is "five hundred sixty-one million, three hundred ninety-eight thousand, four hundred".