409348800 has 504 divisors, whose sum is σ = 1729508352. Its totient is φ = 89856000.

The previous prime is 409348789. The next prime is 409348801. The reversal of 409348800 is 8843904.

It is a tau number, because it is divible by the number of its divisors (504).

It is a super-2 number, since 2×409348800² = 335132880122880000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (409348801) 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 71 ways as a sum of consecutive naturals, for example, 3124735 + ... + 3124865.

Almost surely, 2^409348800 is an apocalyptic number.

409348800 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 409348800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (864754176).

409348800 is an abundant number, since it is smaller than the sum of its proper divisors (1320159552).

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

409348800 is a wasteful number, since it uses less digits than its factorization.

409348800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 197 (or 179 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 36.

The square root of 409348800 is about 20232.3701033764. The cubic root of 409348800 is about 742.5023636969.

The spelling of 409348800 in words is "four hundred nine million, three hundred forty-eight thousand, eight hundred".