76838400 has 360 divisors, whose sum is σ = 296833680. Its totient is φ = 18923520.

The previous prime is 76838383. The next prime is 76838449. The reversal of 76838400 is 483867.

It is a tau number, because it is divible by the number of its divisors (360).

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 35 ways as a sum of consecutive naturals, for example, 2649586 + ... + 2649614.

It is an arithmetic number, because the mean of its divisors is an integer number (824538).

Almost surely, 2^76838400 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 76838400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (148416840).

76838400 is an abundant number, since it is smaller than the sum of its proper divisors (219995280).

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

76838400 is a wasteful number, since it uses less digits than its factorization.

76838400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 86 (or 62 counting only the distinct ones).

The product of its (nonzero) digits is 32256, while the sum is 36.

The square root of 76838400 is about 8765.7515365198. The cubic root of 76838400 is about 425.1342597736.

The spelling of 76838400 in words is "seventy-six million, eight hundred thirty-eight thousand, four hundred".