413144431200 has 288 divisors, whose sum is σ = 1582101551520. Its totient is φ = 103691059200.

The previous prime is 413144431181. The next prime is 413144431237. The reversal of 413144431200 is 2134441314.

413144431200 is a `hidden beast` number, since 4 + 1 + 3 + 14 + 443 + 1 + 200 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 195361 + ... + 929760.

It is an arithmetic number, because the mean of its divisors is an integer number (5493408165).

Almost surely, 2^413144431200 is an apocalyptic number.

413144431200 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 413144431200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (791050775760).

413144431200 is an abundant number, since it is smaller than the sum of its proper divisors (1168957120320).

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

413144431200 is a wasteful number, since it uses less digits than its factorization.

413144431200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1125167 (or 1125148 counting only the distinct ones).

The product of its (nonzero) digits is 4608, while the sum is 27.

Adding to 413144431200 its reverse (2134441314), we get a palindrome (415278872514).

The spelling of 413144431200 in words is "four hundred thirteen billion, one hundred forty-four million, four hundred thirty-one thousand, two hundred".