413584704 has 420 divisors, whose sum is σ = 1475416404. Its totient is φ = 113467392.

The previous prime is 413584681. The next prime is 413584709. The reversal of 413584704 is 407485314.

413584704 is a `hidden beast` number, since 4 + 1 + 3 + 584 + 70 + 4 = 666.

It can be written as a sum of positive squares in 2 ways, for example, as 187142400 + 226442304 = 13680^2 + 15048^2 .

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413584709) by changing a digit.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 21767607 + ... + 21767625.

Almost surely, 2^413584704 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 413584704, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (737708202).

413584704 is an abundant number, since it is smaller than the sum of its proper divisors (1061831700).

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

413584704 is a wasteful number, since it uses less digits than its factorization.

413584704 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 92 (or 54 counting only the distinct ones).

The product of its (nonzero) digits is 53760, while the sum is 36.

The square root of 413584704 is about 20336.7820463317. The cubic root of 413584704 is about 745.0546956225.

The spelling of 413584704 in words is "four hundred thirteen million, five hundred eighty-four thousand, seven hundred four".