413078450400 has 1728 divisors, whose sum is σ = 1886855233536. Its totient is φ = 82561536000.

The previous prime is 413078450399. The next prime is 413078450429. The reversal of 413078450400 is 4054870314.

413078450400 is a `hidden beast` number, since 4 + 130 + 78 + 4 + 50 + 400 = 666.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 2162714305 + ... + 2162714495.

It is an arithmetic number, because the mean of its divisors is an integer number (1091930112).

Almost surely, 2^413078450400 is an apocalyptic number.

413078450400 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 413078450400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (943427616768).

413078450400 is an abundant number, since it is smaller than the sum of its proper divisors (1473776783136).

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

413078450400 is a wasteful number, since it uses less digits than its factorization.

413078450400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 365 (or 349 counting only the distinct ones).

The product of its (nonzero) digits is 53760, while the sum is 36.

The spelling of 413078450400 in words is "four hundred thirteen billion, seventy-eight million, four hundred fifty thousand, four hundred".