77664 has 24 divisors (see below), whose sum is σ = 204120. Its totient is φ = 25856.

The previous prime is 77659. The next prime is 77681. The reversal of 77664 is 46677.

It is a tau number, because it is divible by the number of its divisors (24).

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 nialpdrome in base 10.

It is a zygodrome in base 7.

It is a congruent number.

It is an unprimeable number.

77664 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 3 ways as a sum of consecutive naturals, for example, 309 + ... + 500.

It is an arithmetic number, because the mean of its divisors is an integer number (8505).

2⁷⁷⁶⁶⁴ is an apocalyptic number.

It is an amenable number.

77664 is an abundant number, since it is smaller than the sum of its proper divisors (126456).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (102060).

77664 is a wasteful number, since it uses less digits than its factorization.

77664 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 822 (or 814 counting only the distinct ones).

The product of its digits is 7056, while the sum is 30.

The square root of 77664 is about 278.6826151736. The cubic root of 77664 is about 42.6651475154.

It can be divided in two parts, 77 and 664, that added together give a triangular number (741 = T₃₈).

The spelling of 77664 in words is "seventy-seven thousand, six hundred sixty-four".