413221434400 has 144 divisors (see below), whose sum is σ = 1092958108704. Its totient is φ = 151947694080.

The previous prime is 413221434397. The next prime is 413221434403. The reversal of 413221434400 is 4434122314.

It is an interprime number because it is at equal distance from previous prime (413221434397) and next prime (413221434403).

It is not an unprimeable number, because it can be changed into a prime (413221434403) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 231499 + ... + 938101.

It is an arithmetic number, because the mean of its divisors is an integer number (7589986866).

Almost surely, 2^413221434400 is an apocalyptic number.

413221434400 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 413221434400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (546479054352).

413221434400 is an abundant number, since it is smaller than the sum of its proper divisors (679736674304).

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

413221434400 is a wasteful number, since it uses less digits than its factorization.

413221434400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 706683 (or 706670 counting only the distinct ones).

The product of its (nonzero) digits is 9216, while the sum is 28.

Adding to 413221434400 its reverse (4434122314), we get a palindrome (417655556714).

It can be divided in two parts, 4132214 and 34400, that added together give a palindrome (4166614).

The spelling of 413221434400 in words is "four hundred thirteen billion, two hundred twenty-one million, four hundred thirty-four thousand, four hundred".