413452800 has 360 divisors, whose sum is σ = 1535289756. Its totient is φ = 106168320.

The previous prime is 413452789. The next prime is 413452817. The reversal of 413452800 is 8254314.

413452800 is a `hidden beast` number, since 4 + 134 + 528 + 0 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 231526656 + 181926144 = 15216^2 + 13488^2 .

It is a tau number, because it is divible by the number of its divisors (360).

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 4262352 + ... + 4262448.

Almost surely, 2^413452800 is an apocalyptic number.

413452800 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 413452800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (767644878).

413452800 is an abundant number, since it is smaller than the sum of its proper divisors (1121836956).

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

413452800 is a wasteful number, since it uses less digits than its factorization.

413452800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 168 (or 144 counting only the distinct ones).

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

The square root of 413452800 is about 20333.5387967761. The cubic root of 413452800 is about 744.9754807780.

The spelling of 413452800 in words is "four hundred thirteen million, four hundred fifty-two thousand, eight hundred".