413008409520000 has 1280 divisors, whose sum is σ = 1796954470502400. Its totient is φ = 91356595200000.

The previous prime is 413008409519977. The next prime is 413008409520029. The reversal of 413008409520000 is 25904800314.

413008409520000 is a `hidden beast` number, since 41 + 3 + 0 + 0 + 8 + 409 + 5 + 200 + 0 + 0 = 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 159 ways as a sum of consecutive naturals, for example, 468279430 + ... + 469160570.

It is an arithmetic number, because the mean of its divisors is an integer number (1403870680080).

Almost surely, 2^{413008409520000} is an apocalyptic number.

413008409520000 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 413008409520000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (898477235251200).

413008409520000 is an abundant number, since it is smaller than the sum of its proper divisors (1383946060982400).

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

413008409520000 is an equidigital number, since it uses as much as digits as its factorization.

413008409520000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 881222 (or 881189 counting only the distinct ones).

The product of its (nonzero) digits is 34560, while the sum is 36.

The spelling of 413008409520000 in words is "four hundred thirteen trillion, eight billion, four hundred nine million, five hundred twenty thousand".