413830348800 has 864 divisors, whose sum is σ = 1544672384640. Its totient is φ = 96888422400.

The previous prime is 413830348753. The next prime is 413830348823. The reversal of 413830348800 is 8843038314.

It is a super-3 number, since 3×413830348800³ (a number of 36 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 4649779156 + ... + 4649779244.

It is an arithmetic number, because the mean of its divisors is an integer number (1787815260).

Almost surely, 2^413830348800 is an apocalyptic number.

413830348800 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 413830348800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (772336192320).

413830348800 is an abundant number, since it is smaller than the sum of its proper divisors (1130842035840).

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

413830348800 is an equidigital number, since it uses as much as digits as its factorization.

413830348800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 190 (or 153 counting only the distinct ones).

The product of its (nonzero) digits is 221184, while the sum is 42.

The spelling of 413830348800 in words is "four hundred thirteen billion, eight hundred thirty million, three hundred forty-eight thousand, eight hundred".