409054800 has 480 divisors, whose sum is σ = 1727032320. Its totient is φ = 80179200.

The previous prime is 409054787. The next prime is 409054813. The reversal of 409054800 is 8450904.

It is an interprime number because it is at equal distance from previous prime (409054787) and next prime (409054813).

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 95 ways as a sum of consecutive naturals, for example, 1755484 + ... + 1755716.

It is an arithmetic number, because the mean of its divisors is an integer number (3597984).

Almost surely, 2^409054800 is an apocalyptic number.

409054800 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 409054800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (863516160).

409054800 is an abundant number, since it is smaller than the sum of its proper divisors (1317977520).

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

409054800 is a wasteful number, since it uses less digits than its factorization.

409054800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 291 (or 280 counting only the distinct ones).

The product of its (nonzero) digits is 5760, while the sum is 30.

The square root of 409054800 is about 20225.1032135809. The cubic root of 409054800 is about 742.3245626164.

The spelling of 409054800 in words is "four hundred nine million, fifty-four thousand, eight hundred".