77640 has 32 divisors (see below), whose sum is σ = 233280. Its totient is φ = 20672.

The previous prime is 77621. The next prime is 77641. The reversal of 77640 is 4677.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a nialpdrome in base 10.

It is a zygodrome in base 7.

It is a self number, because there is not a number n which added to its sum of digits gives 77640.

It is not an unprimeable number, because it can be changed into a prime (77641) by changing a digit.

77640 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 7 ways as a sum of consecutive naturals, for example, 204 + ... + 443.

It is an arithmetic number, because the mean of its divisors is an integer number (7290).

2⁷⁷⁶⁴⁰ is an apocalyptic number.

It is an amenable number.

77640 is an abundant number, since it is smaller than the sum of its proper divisors (155640).

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 (116640).

77640 is a wasteful number, since it uses less digits than its factorization.

77640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 661 (or 657 counting only the distinct ones).

The product of its (nonzero) digits is 1176, while the sum is 24.

The square root of 77640 is about 278.6395521099. The cubic root of 77640 is about 42.6607522184.

It can be divided in two parts, 77 and 640, that added together give a palindrome (717).

The spelling of 77640 in words is "seventy-seven thousand, six hundred forty".