409209840 has 480 divisors, whose sum is σ = 1633824000. Its totient is φ = 93809664.

The previous prime is 409209811. The next prime is 409209851. The reversal of 409209840 is 48902904.

It is a happy number.

409209840 is a `hidden beast` number, since 409 + 209 + 8 + 40 = 666.

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

It is a junction number, because it is equal to n+sod(n) for n = 409209795 and 409209804.

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, 6935731 + ... + 6935789.

It is an arithmetic number, because the mean of its divisors is an integer number (3403800).

Almost surely, 2^409209840 is an apocalyptic number.

409209840 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 409209840, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (816912000).

409209840 is an abundant number, since it is smaller than the sum of its proper divisors (1224614160).

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

409209840 is a wasteful number, since it uses less digits than its factorization.

409209840 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 126 (or 101 counting only the distinct ones).

The product of its (nonzero) digits is 20736, while the sum is 36.

The square root of 409209840 is about 20228.9357110057. The cubic root of 409209840 is about 742.4183360853.

The spelling of 409209840 in words is "four hundred nine million, two hundred nine thousand, eight hundred forty".