77688 has 48 divisors (see below), whose sum is σ = 229320. Its totient is φ = 23616.

The previous prime is 77687. The next prime is 77689. The reversal of 77688 is 88677.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (77687) and next prime (77689).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 77688.

It is not an unprimeable number, because it can be changed into a prime (77681) 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, 895 + ... + 977.

2⁷⁷⁶⁸⁸ is an apocalyptic number.

77688 is a gapful number since it is divisible by the number (78) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 77688, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (114660).

77688 is an abundant number, since it is smaller than the sum of its proper divisors (151632).

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

77688 is a wasteful number, since it uses less digits than its factorization.

77688 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 108 (or 101 counting only the distinct ones).

The product of its digits is 18816, while the sum is 36.

The square root of 77688 is about 278.7256715841. The cubic root of 77688 is about 42.6695419069.

It can be divided in two parts, 7768 and 8, that added together give a 5-th power (7776 = 6⁵).

The spelling of 77688 in words is "seventy-seven thousand, six hundred eighty-eight".