413328000 has 256 divisors, whose sum is σ = 1400256000. Its totient is φ = 107827200.

The previous prime is 413327989. The next prime is 413328001. The reversal of 413328000 is 823314.

It is a happy number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413328001) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 3791946 + ... + 3792054.

It is an arithmetic number, because the mean of its divisors is an integer number (5469750).

Almost surely, 2^413328000 is an apocalyptic number.

413328000 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 413328000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (700128000).

413328000 is an abundant number, since it is smaller than the sum of its proper divisors (986928000).

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

413328000 is a wasteful number, since it uses less digits than its factorization.

413328000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 220 (or 198 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 21.

The square root of 413328000 is about 20330.4697437123. The cubic root of 413328000 is about 744.9005167223.

The spelling of 413328000 in words is "four hundred thirteen million, three hundred twenty-eight thousand".