407664000 has 384 divisors, whose sum is σ = 1551420000. Its totient is φ = 102297600.

The previous prime is 407663989. The next prime is 407664007. The reversal of 407664000 is 466704.

It is a tau number, because it is divible by the number of its divisors (384).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (407664007) by changing a digit.

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 47 ways as a sum of consecutive naturals, for example, 2735926 + ... + 2736074.

Almost surely, 2^407664000 is an apocalyptic number.

407664000 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 407664000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (775710000).

407664000 is an abundant number, since it is smaller than the sum of its proper divisors (1143756000).

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

407664000 is a wasteful number, since it uses less digits than its factorization.

407664000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 203 (or 178 counting only the distinct ones).

The product of its (nonzero) digits is 4032, while the sum is 27.

The square root of 407664000 is about 20190.6909242849. The cubic root of 407664000 is about 741.4822978717.

The spelling of 407664000 in words is "four hundred seven million, six hundred sixty-four thousand".