77688000 has 336 divisors, whose sum is σ = 302885856. Its totient is φ = 18892800.

The previous prime is 77687999. The next prime is 77688029. The reversal of 77688000 is 88677.

It is a happy number.

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

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 935959 + ... + 936041.

It is an arithmetic number, because the mean of its divisors is an integer number (901446).

Almost surely, 2^77688000 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 77688000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (151442928).

77688000 is an abundant number, since it is smaller than the sum of its proper divisors (225197856).

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

77688000 is a wasteful number, since it uses less digits than its factorization.

77688000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 129 (or 106 counting only the distinct ones).

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

The square root of 77688000 is about 8814.0796456578. The cubic root of 77688000 is about 426.6954190693.

The spelling of 77688000 in words is "seventy-seven million, six hundred eighty-eight thousand".