413089955776800 has 432 divisors, whose sum is σ = 1493014997361888. Its totient is φ = 107416447488000.

The previous prime is 413089955776793. The next prime is 413089955776837. The reversal of 413089955776800 is 8677559980314.

413089955776800 is a `hidden beast` number, since 4 + 1 + 3 + 0 + 8 + 9 + 9 + 557 + 7 + 68 + 0 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (72).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 184959559 + ... + 187179641.

It is an arithmetic number, because the mean of its divisors is an integer number (3456053234634).

Almost surely, 2^{413089955776800} is an apocalyptic number.

413089955776800 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 413089955776800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (746507498680944).

413089955776800 is an abundant number, since it is smaller than the sum of its proper divisors (1079925041585088).

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

413089955776800 is a wasteful number, since it uses less digits than its factorization.

413089955776800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2220753 (or 2220737 counting only the distinct ones).

The product of its (nonzero) digits is 457228800, while the sum is 72.

The spelling of 413089955776800 in words is "four hundred thirteen trillion, eighty-nine billion, nine hundred fifty-five million, seven hundred seventy-six thousand, eight hundred".