413212800 has 768 divisors, whose sum is σ = 1869880320. Its totient is φ = 77414400.

The previous prime is 413212799. The next prime is 413212823. The reversal of 413212800 is 8212314.

It is a Harshad number since it is a multiple of its sum of digits (21).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 9609579 + ... + 9609621.

It is an arithmetic number, because the mean of its divisors is an integer number (2434740).

Almost surely, 2^413212800 is an apocalyptic number.

413212800 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 413212800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (934940160).

413212800 is an abundant number, since it is smaller than the sum of its proper divisors (1456667520).

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

413212800 is a wasteful number, since it uses less digits than its factorization.

413212800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 101 (or 84 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 21.

The square root of 413212800 is about 20327.6363603839. The cubic root of 413212800 is about 744.8313057380.

The spelling of 413212800 in words is "four hundred thirteen million, two hundred twelve thousand, eight hundred".