413269516800 has 2160 divisors, whose sum is σ = 1897492808640. Its totient is φ = 87071293440.

The previous prime is 413269516799. The next prime is 413269516811. The reversal of 413269516800 is 8615962314.

413269516800 is a `hidden beast` number, since 41 + 32 + 69 + 516 + 8 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (2160).

It is a super-2 number, since 2×413269516800² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

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 215 ways as a sum of consecutive naturals, for example, 11169446382 + ... + 11169446418.

Almost surely, 2^413269516800 is an apocalyptic number.

413269516800 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 413269516800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (948746404320).

413269516800 is an abundant number, since it is smaller than the sum of its proper divisors (1484223291840).

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

413269516800 is an frugal number, since it uses more digits than its factorization.

413269516800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 115 (or 73 counting only the distinct ones).

The product of its (nonzero) digits is 311040, while the sum is 45.

The spelling of 413269516800 in words is "four hundred thirteen billion, two hundred sixty-nine million, five hundred sixteen thousand, eight hundred".