413402024000 has 168 divisors, whose sum is σ = 1190940647832. Its totient is φ = 141737702400.

The previous prime is 413402023987. The next prime is 413402024011. The reversal of 413402024000 is 420204314.

It can be written as a sum of positive squares in 4 ways, for example, as 36081762304 + 377320261696 = 189952^2 + 614264^2 .

It is a Harshad number since it is a multiple of its sum of digits (20).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 135299 + ... + 919298.

Almost surely, 2^413402024000 is an apocalyptic number.

413402024000 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 413402024000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (595470323916).

413402024000 is an abundant number, since it is smaller than the sum of its proper divisors (777538623832).

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

413402024000 is a wasteful number, since it uses less digits than its factorization.

413402024000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1054638 (or 1054611 counting only the distinct ones).

The product of its (nonzero) digits is 768, while the sum is 20.

Adding to 413402024000 its reverse (420204314), we get a palindrome (413822228314).

The spelling of 413402024000 in words is "four hundred thirteen billion, four hundred two million, twenty-four thousand".