413828382844800 has 3840 divisors, whose sum is σ = 1942969267008000. Its totient is φ = 84238191820800.

The previous prime is 413828382844787. The next prime is 413828382844813. The reversal of 413828382844800 is 8448283828314.

413828382844800 is a `hidden beast` number, since 4 + 1 + 38 + 2 + 83 + 82 + 8 + 448 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (413828382844787) and next prime (413828382844813).

It is a Harshad number since it is a multiple of its sum of digits (63).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 479 ways as a sum of consecutive naturals, for example, 538138338816 + ... + 538138339584.

It is an arithmetic number, because the mean of its divisors is an integer number (505981579950).

Almost surely, 2^{413828382844800} is an apocalyptic number.

413828382844800 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 413828382844800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (971484633504000).

413828382844800 is an abundant number, since it is smaller than the sum of its proper divisors (1529140884163200).

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

413828382844800 is a wasteful number, since it uses less digits than its factorization.

413828382844800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1339 (or 1313 counting only the distinct ones).

The product of its (nonzero) digits is 75497472, while the sum is 63.

The spelling of 413828382844800 in words is "four hundred thirteen trillion, eight hundred twenty-eight billion, three hundred eighty-two million, eight hundred forty-four thousand, eight hundred".