413688254400 has 1176 divisors, whose sum is σ = 1670582611584. Its totient is φ = 100329062400.

The previous prime is 413688254393. The next prime is 413688254423. The reversal of 413688254400 is 4452886314.

413688254400 is a `hidden beast` number, since 41 + 3 + 68 + 8 + 2 + 544 + 0 + 0 = 666.

It is a super-2 number, since 2×413688254400² (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 a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 167 ways as a sum of consecutive naturals, for example, 614692464 + ... + 614693136.

Almost surely, 2^413688254400 is an apocalyptic number.

413688254400 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 413688254400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (835291305792).

413688254400 is an abundant number, since it is smaller than the sum of its proper divisors (1256894357184).

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

413688254400 is a wasteful number, since it uses less digits than its factorization.

413688254400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 761 (or 731 counting only the distinct ones).

The product of its (nonzero) digits is 737280, while the sum is 45.

The spelling of 413688254400 in words is "four hundred thirteen billion, six hundred eighty-eight million, two hundred fifty-four thousand, four hundred".