409328400 has 240 divisors, whose sum is σ = 1487474240. Its totient is φ = 95385600.

The previous prime is 409328383. The next prime is 409328407. The reversal of 409328400 is 4823904.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (240).

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

It is not an unprimeable number, because it can be changed into a prime (409328407) 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 47 ways as a sum of consecutive naturals, for example, 295710 + ... + 297090.

Almost surely, 2^409328400 is an apocalyptic number.

409328400 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 409328400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (743737120).

409328400 is an abundant number, since it is smaller than the sum of its proper divisors (1078145840).

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

409328400 is a wasteful number, since it uses less digits than its factorization.

409328400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1434 (or 1423 counting only the distinct ones).

The product of its (nonzero) digits is 6912, while the sum is 30.

The square root of 409328400 is about 20231.8659544788. The cubic root of 409328400 is about 742.4900292282.

The spelling of 409328400 in words is "four hundred nine million, three hundred twenty-eight thousand, four hundred".