413795200 has 384 divisors, whose sum is σ = 1328040000. Its totient is φ = 126443520.

The previous prime is 413795183. The next prime is 413795203. The reversal of 413795200 is 2597314.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413795203) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 14268786 + ... + 14268814.

Almost surely, 2^413795200 is an apocalyptic number.

413795200 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 413795200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (664020000).

413795200 is an abundant number, since it is smaller than the sum of its proper divisors (914244800).

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

413795200 is a wasteful number, since it uses less digits than its factorization.

413795200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 87 (or 56 counting only the distinct ones).

The product of its (nonzero) digits is 7560, while the sum is 31.

The square root of 413795200 is about 20341.9566413853. The cubic root of 413795200 is about 745.1810739537.

The spelling of 413795200 in words is "four hundred thirteen million, seven hundred ninety-five thousand, two hundred".