409728000 has 352 divisors, whose sum is σ = 1502137728. Its totient is φ = 98304000.

The previous prime is 409727993. The next prime is 409728017. The reversal of 409728000 is 827904.

It is a tau number, because it is divible by the number of its divisors (352).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 4223952 + ... + 4224048.

Almost surely, 2^409728000 is an apocalyptic number.

409728000 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 409728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (751068864).

409728000 is an abundant number, since it is smaller than the sum of its proper divisors (1092409728).

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

409728000 is a wasteful number, since it uses less digits than its factorization.

409728000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 146 (or 118 counting only the distinct ones).

The product of its (nonzero) digits is 4032, while the sum is 30.

The square root of 409728000 is about 20241.7390557234. The cubic root of 409728000 is about 742.7315651350.

The spelling of 409728000 in words is "four hundred nine million, seven hundred twenty-eight thousand".