413520408 has 288 divisors, whose sum is σ = 1422720000. Its totient is φ = 107775360.

The previous prime is 413520407. The next prime is 413520421. The reversal of 413520408 is 804025314.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413520407) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 2077893 + ... + 2078091.

It is an arithmetic number, because the mean of its divisors is an integer number (4940000).

Almost surely, 2^413520408 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413520408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (711360000).

413520408 is an abundant number, since it is smaller than the sum of its proper divisors (1009199592).

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

413520408 is a wasteful number, since it uses less digits than its factorization.

413520408 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 275 (or 261 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 27.

The square root of 413520408 is about 20335.2012038239. The cubic root of 413520408 is about 745.0160848140.

The spelling of 413520408 in words is "four hundred thirteen million, five hundred twenty thousand, four hundred eight".