76838051908800 has 6720 divisors, whose sum is σ = 404740874926080. Its totient is φ = 13811012075520.

The previous prime is 76838051908759. The next prime is 76838051908811. The reversal of 76838051908800 is 880915083867.

76838051908800 is a `hidden beast` number, since 7 + 6 + 8 + 38 + 0 + 519 + 0 + 8 + 80 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (6720).

It is a super-2 number, since 2×76838051908800² (a number of 29 digits) contains 22 as substring.

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

It is an unprimeable number.

It is a polite number, since it can be written in 959 ways as a sum of consecutive naturals, for example, 87614653962 + ... + 87614654838.

It is an arithmetic number, because the mean of its divisors is an integer number (60229296864).

Almost surely, 2^{76838051908800} is an apocalyptic number.

76838051908800 is a gapful number since it is divisible by the number (70) 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 76838051908800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (202370437463040).

76838051908800 is an abundant number, since it is smaller than the sum of its proper divisors (327902823017280).

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

76838051908800 is a wasteful number, since it uses less digits than its factorization.

76838051908800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 990 (or 966 counting only the distinct ones).

The product of its (nonzero) digits is 23224320, while the sum is 63.

The spelling of 76838051908800 in words is "seventy-six trillion, eight hundred thirty-eight billion, fifty-one million, nine hundred eight thousand, eight hundred".