77880 has 64 divisors (see below), whose sum is σ = 259200. Its totient is φ = 18560.

The previous prime is 77867. The next prime is 77893. The reversal of 77880 is 8877.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (77867) and next prime (77893).

It is a Smith number, since the sum of its digits (30) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

77880 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 15 ways as a sum of consecutive naturals, for example, 1291 + ... + 1349.

It is an arithmetic number, because the mean of its divisors is an integer number (4050).

2⁷⁷⁸⁸⁰ 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 77880, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (129600).

77880 is an abundant number, since it is smaller than the sum of its proper divisors (181320).

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

77880 is a wasteful number, since it uses less digits than its factorization.

77880 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 84 (or 80 counting only the distinct ones).

The product of its (nonzero) digits is 3136, while the sum is 30.

The square root of 77880 is about 279.0698837209. The cubic root of 77880 is about 42.7046645008.

It can be divided in two parts, 778 and 80, that added together give a palindrome (858).

The spelling of 77880 in words is "seventy-seven thousand, eight hundred eighty".