77728 has 24 divisors (see below), whose sum is σ = 175392. Its totient is φ = 33216.

The previous prime is 77723. The next prime is 77731. The reversal of 77728 is 82777.

It is a Smith number, since the sum of its digits (31) coincides with the sum of the digits of its prime factors.

It is a nude number because it is divisible by every one of its digits.

It is a self number, because there is not a number n which added to its sum of digits gives 77728.

It is not an unprimeable number, because it can be changed into a prime (77723) by changing a digit.

77728 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 3 ways as a sum of consecutive naturals, for example, 51 + ... + 397.

It is an arithmetic number, because the mean of its divisors is an integer number (7308).

2⁷⁷⁷²⁸ 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 77728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (87696).

77728 is an abundant number, since it is smaller than the sum of its proper divisors (97664).

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

77728 is a wasteful number, since it uses less digits than its factorization.

77728 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 364 (or 356 counting only the distinct ones).

The product of its digits is 5488, while the sum is 31.

The square root of 77728 is about 278.7974174916. The cubic root of 77728 is about 42.6768638821.

The spelling of 77728 in words is "seventy-seven thousand, seven hundred twenty-eight".