413251372800 has 1080 divisors, whose sum is σ = 1784151806976. Its totient is φ = 92409569280.

The previous prime is 413251372771. The next prime is 413251372817. The reversal of 413251372800 is 8273152314.

413251372800 is a `hidden beast` number, since 4 + 132 + 513 + 7 + 2 + 8 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1080).

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 119 ways as a sum of consecutive naturals, for example, 170552389 + ... + 170554811.

Almost surely, 2^413251372800 is an apocalyptic number.

413251372800 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 413251372800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (892075903488).

413251372800 is an abundant number, since it is smaller than the sum of its proper divisors (1370900434176).

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

413251372800 is a wasteful number, since it uses less digits than its factorization.

413251372800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2515 (or 2487 counting only the distinct ones).

The product of its (nonzero) digits is 40320, while the sum is 36.

The spelling of 413251372800 in words is "four hundred thirteen billion, two hundred fifty-one million, three hundred seventy-two thousand, eight hundred".