415900800 has 288 divisors, whose sum is σ = 1696855680. Its totient is φ = 95016960.

The previous prime is 415900769. The next prime is 415900817. The reversal of 415900800 is 8009514.

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

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 200569 + ... + 202631.

It is an arithmetic number, because the mean of its divisors is an integer number (5891860).

Almost surely, 2^415900800 is an apocalyptic number.

415900800 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 415900800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (848427840).

415900800 is an abundant number, since it is smaller than the sum of its proper divisors (1280954880).

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

415900800 is a wasteful number, since it uses less digits than its factorization.

415900800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2100 (or 2080 counting only the distinct ones).

The product of its (nonzero) digits is 1440, while the sum is 27.

The square root of 415900800 is about 20393.6460693031. The cubic root of 415900800 is about 746.4428892894.

The spelling of 415900800 in words is "four hundred fifteen million, nine hundred thousand, eight hundred".