413641800 has 288 divisors, whose sum is σ = 1633020480. Its totient is φ = 92505600.

The previous prime is 413641769. The next prime is 413641817. The reversal of 413641800 is 8146314.

413641800 is a `hidden beast` number, since 4 + 13 + 641 + 8 + 0 + 0 = 666.

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 71 ways as a sum of consecutive naturals, for example, 256597 + ... + 258203.

It is an arithmetic number, because the mean of its divisors is an integer number (5670210).

Almost surely, 2^413641800 is an apocalyptic number.

413641800 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 413641800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (816510240).

413641800 is an abundant number, since it is smaller than the sum of its proper divisors (1219378680).

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

413641800 is a wasteful number, since it uses less digits than its factorization.

413641800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1653 (or 1641 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The square root of 413641800 is about 20338.1857597968. The cubic root of 413641800 is about 745.0889793577.

The spelling of 413641800 in words is "four hundred thirteen million, six hundred forty-one thousand, eight hundred".