77760 has 84 divisors (see below), whose sum is σ = 277368. Its totient is φ = 20736.

The previous prime is 77747. The next prime is 77761. The reversal of 77760 is 6777.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a nialpdrome in base 10.

It is a zygodrome in base 8.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (77761) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 15550 + ... + 15554.

It is an arithmetic number, because the mean of its divisors is an integer number (3302).

2⁷⁷⁷⁶⁰ 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 77760, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (138684).

77760 is an abundant number, since it is smaller than the sum of its proper divisors (199608).

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

77760 is an equidigital number, since it uses as much as digits as its factorization.

77760 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 32 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 2058, while the sum is 27.

The square root of 77760 is about 278.8548009269. The cubic root of 77760 is about 42.6827196539.

The spelling of 77760 in words is "seventy-seven thousand, seven hundred sixty".