413564800 has 192 divisors, whose sum is σ = 1153497600. Its totient is φ = 145152000.

The previous prime is 413564761. The next prime is 413564819. The reversal of 413564800 is 8465314.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (31).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1091011 + ... + 1091389.

It is an arithmetic number, because the mean of its divisors is an integer number (6007800).

Almost surely, 2^413564800 is an apocalyptic number.

413564800 is a gapful number since it is divisible by the number (40) 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 413564800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (576748800).

413564800 is an abundant number, since it is smaller than the sum of its proper divisors (739932800).

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

413564800 is a wasteful number, since it uses less digits than its factorization.

413564800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 445 (or 428 counting only the distinct ones).

The product of its (nonzero) digits is 11520, while the sum is 31.

The square root of 413564800 is about 20336.2926808207. The cubic root of 413564800 is about 745.0427433699.

The spelling of 413564800 in words is "four hundred thirteen million, five hundred sixty-four thousand, eight hundred".