409380480 has 320 divisors, whose sum is σ = 1499553000. Its totient is φ = 106389504.

The previous prime is 409380467. The next prime is 409380529. The reversal of 409380480 is 84083904.

It can be written as a sum of positive squares in 4 ways, for example, as 291180096 + 118200384 = 17064^2 + 10872^2 .

It is a tau number, because it is divible by the number of its divisors (320).

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

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 39 ways as a sum of consecutive naturals, for example, 2747446 + ... + 2747594.

Almost surely, 2^409380480 is an apocalyptic number.

409380480 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 409380480, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (749776500).

409380480 is an abundant number, since it is smaller than the sum of its proper divisors (1090172520).

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

409380480 is a wasteful number, since it uses less digits than its factorization.

409380480 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 233 (or 212 counting only the distinct ones).

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

The square root of 409380480 is about 20233.1529920574. The cubic root of 409380480 is about 742.5215175888.

The spelling of 409380480 in words is "four hundred nine million, three hundred eighty thousand, four hundred eighty".