77568 has 36 divisors (see below), whose sum is σ = 208488. Its totient is φ = 25600.

The previous prime is 77563. The next prime is 77569. The reversal of 77568 is 86577.

Its product of digits (11760) is a multiple of the sum of its prime factors (120).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (77563) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 718 + ... + 818.

2⁷⁷⁵⁶⁸ 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 77568, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (104244).

77568 is an abundant number, since it is smaller than the sum of its proper divisors (130920).

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

77568 is a wasteful number, since it uses less digits than its factorization.

77568 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 120 (or 106 counting only the distinct ones).

The product of its digits is 11760, while the sum is 33.

The square root of 77568 is about 278.5103229685. The cubic root of 77568 is about 42.6475608903.

Subtracting 77568 from its reverse (86577), we obtain a palindrome (9009).

The spelling of 77568 in words is "seventy-seven thousand, five hundred sixty-eight".