76800 has 66 divisors (see below), whose sum is σ = 253828. Its totient is φ = 20480.

The previous prime is 76781. The next prime is 76801. The reversal of 76800 is 867.

It is not an unprimeable number, because it can be changed into a prime (76801) by changing a digit.

76800 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 15358 + ... + 15362.

2⁷⁶⁸⁰⁰ 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 76800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (126914).

76800 is an abundant number, since it is smaller than the sum of its proper divisors (177028).

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

76800 is a wasteful number, since it uses less digits than its factorization.

76800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 33 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 336, while the sum is 21.

The square root of 76800 is about 277.1281292110. The cubic root of 76800 is about 42.5063427673.

Multiplying 76800 by its reverse (867), we get a square (66585600 = 8160²).

The spelling of 76800 in words is "seventy-six thousand, eight hundred".