409407600 has 480 divisors, whose sum is σ = 1647323136. Its totient is φ = 84787200.

The previous prime is 409407599. The next prime is 409407637. The reversal of 409407600 is 6704904.

It is a super-2 number, since 2×409407600² = 335229165875520000, which contains 22 as substring.

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 pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 6711570 + ... + 6711630.

Almost surely, 2^409407600 is an apocalyptic number.

409407600 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 409407600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (823661568).

409407600 is an abundant number, since it is smaller than the sum of its proper divisors (1237915536).

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

409407600 is a wasteful number, since it uses less digits than its factorization.

409407600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 153 (or 142 counting only the distinct ones).

The product of its (nonzero) digits is 6048, while the sum is 30.

The square root of 409407600 is about 20233.8231681509. The cubic root of 409407600 is about 742.5379136962.

The spelling of 409407600 in words is "four hundred nine million, four hundred seven thousand, six hundred".