890416800 has 720 divisors, whose sum is σ = 4022992512. Its totient is φ = 186624000.

The previous prime is 890416799. The next prime is 890416819. The reversal of 890416800 is 8614098.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (720).

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 5896725 + ... + 5896875.

Almost surely, 2^890416800 is an apocalyptic number.

890416800 is a gapful number since it is divisible by the number (80) 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 890416800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2011496256).

890416800 is an abundant number, since it is smaller than the sum of its proper divisors (3132575712).

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

890416800 is a wasteful number, since it uses less digits than its factorization.

890416800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 203 (or 181 counting only the distinct ones).

The product of its (nonzero) digits is 13824, while the sum is 36.

The square root of 890416800 is about 29839.8525465526. The cubic root of 890416800 is about 962.0503054737.

The spelling of 890416800 in words is "eight hundred ninety million, four hundred sixteen thousand, eight hundred".