413964000 has 192 divisors, whose sum is σ = 1507222080. Its totient is φ = 110361600.

The previous prime is 413963999. The next prime is 413964007. The reversal of 413964000 is 469314.

413964000 is a `hidden beast` number, since 4 + 13 + 9 + 640 + 0 + 0 = 666.

It is a hoax number, since the sum of its digits (27) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413964007) by changing a digit.

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 31 ways as a sum of consecutive naturals, for example, 106084 + ... + 109916.

It is an arithmetic number, because the mean of its divisors is an integer number (7850115).

Almost surely, 2^413964000 is an apocalyptic number.

413964000 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 413964000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (753611040).

413964000 is an abundant number, since it is smaller than the sum of its proper divisors (1093258080).

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

413964000 is a wasteful number, since it uses less digits than its factorization.

413964000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3867 (or 3843 counting only the distinct ones).

The product of its (nonzero) digits is 2592, while the sum is 27.

The square root of 413964000 is about 20346.1052784065. The cubic root of 413964000 is about 745.2823877316.

The spelling of 413964000 in words is "four hundred thirteen million, nine hundred sixty-four thousand".