409974400 has 192 divisors, whose sum is σ = 1164880800. Its totient is φ = 141004800.

The previous prime is 409974361. The next prime is 409974403. The reversal of 409974400 is 4479904.

It is a self number, because there is not a number n which added to its sum of digits gives 409974400.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (409974403) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 668494 + ... + 669106.

Almost surely, 2^409974400 is an apocalyptic number.

409974400 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 409974400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (582440400).

409974400 is an abundant number, since it is smaller than the sum of its proper divisors (754906400).

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

409974400 is a wasteful number, since it uses less digits than its factorization.

409974400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 667 (or 650 counting only the distinct ones).

The product of its (nonzero) digits is 36288, while the sum is 37.

The square root of 409974400 is about 20247.8245745068. The cubic root of 409974400 is about 742.8804219248.

The spelling of 409974400 in words is "four hundred nine million, nine hundred seventy-four thousand, four hundred".