413083742400 has 504 divisors, whose sum is σ = 1766260404480. Its totient is φ = 89449297920.

The previous prime is 413083742371. The next prime is 413083742431. The reversal of 413083742400 is 4247380314.

413083742400 is a `hidden beast` number, since 4 + 130 + 83 + 7 + 42 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (504).

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

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 1807357 + ... + 2023043.

Almost surely, 2^413083742400 is an apocalyptic number.

413083742400 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 413083742400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (883130202240).

413083742400 is an abundant number, since it is smaller than the sum of its proper divisors (1353176662080).

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

413083742400 is a wasteful number, since it uses less digits than its factorization.

413083742400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 215741 (or 215723 counting only the distinct ones).

The product of its (nonzero) digits is 64512, while the sum is 36.

The spelling of 413083742400 in words is "four hundred thirteen billion, eighty-three million, seven hundred forty-two thousand, four hundred".