413808640 has 192 divisors, whose sum is σ = 1188794880. Its totient is φ = 135168000.

The previous prime is 413808631. The next prime is 413808641. The reversal of 413808640 is 46808314.

It is a junction number, because it is equal to n+sod(n) for n = 413808596 and 413808605.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413808641) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1648515 + ... + 1648765.

It is an arithmetic number, because the mean of its divisors is an integer number (6191640).

Almost surely, 2^413808640 is an apocalyptic number.

413808640 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 413808640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (594397440).

413808640 is an abundant number, since it is smaller than the sum of its proper divisors (774986240).

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

413808640 is a wasteful number, since it uses less digits than its factorization.

413808640 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 308 (or 288 counting only the distinct ones).

The product of its (nonzero) digits is 18432, while the sum is 34.

The square root of 413808640 is about 20342.2869904050. The cubic root of 413808640 is about 745.1891416525.

The spelling of 413808640 in words is "four hundred thirteen million, eight hundred eight thousand, six hundred forty".