413899200 has 672 divisors, whose sum is σ = 1799051520. Its totient is φ = 91238400.

The previous prime is 413899183. The next prime is 413899229. The reversal of 413899200 is 2998314.

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 6177567 + ... + 6177633.

It is an arithmetic number, because the mean of its divisors is an integer number (2677160).

Almost surely, 2^413899200 is an apocalyptic number.

413899200 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 413899200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (899525760).

413899200 is an abundant number, since it is smaller than the sum of its proper divisors (1385152320).

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

413899200 is a wasteful number, since it uses less digits than its factorization.

413899200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 122 (or 101 counting only the distinct ones).

The product of its (nonzero) digits is 15552, while the sum is 36.

The square root of 413899200 is about 20344.5127737186. The cubic root of 413899200 is about 745.2434980223.

The spelling of 413899200 in words is "four hundred thirteen million, eight hundred ninety-nine thousand, two hundred".