413884800 has 288 divisors, whose sum is σ = 1688634480. Its totient is φ = 94556160.

The previous prime is 413884763. The next prime is 413884831. The reversal of 413884800 is 8488314.

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 a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 200574 + ... + 202626.

Almost surely, 2^413884800 is an apocalyptic number.

413884800 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 413884800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (844317240).

413884800 is an abundant number, since it is smaller than the sum of its proper divisors (1274749680).

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

413884800 is a wasteful number, since it uses less digits than its factorization.

413884800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2090 (or 2070 counting only the distinct ones).

The product of its (nonzero) digits is 24576, while the sum is 36.

The square root of 413884800 is about 20344.1588668591. The cubic root of 413884800 is about 745.2348553135.

It can be divided in two parts, 41 and 3884800, that added together give a square (3884841 = 1971²).

The spelling of 413884800 in words is "four hundred thirteen million, eight hundred eighty-four thousand, eight hundred".