77940 has 36 divisors (see below), whose sum is σ = 236964. Its totient is φ = 20736.

The previous prime is 77933. The next prime is 77951. The reversal of 77940 is 4977.

It can be written as a sum of positive squares in 2 ways, for example, as 17424 + 60516 = 132^2 + 246^2 .

It is a tau number, because it is divible by the number of its divisors (36).

It is an Ulam number.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 37 + ... + 396.

2⁷⁷⁹⁴⁰ 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 77940, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (118482).

77940 is an abundant number, since it is smaller than the sum of its proper divisors (159024).

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

77940 is a wasteful number, since it uses less digits than its factorization.

77940 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 448 (or 443 counting only the distinct ones).

The product of its (nonzero) digits is 1764, while the sum is 27.

The square root of 77940 is about 279.1773629792. The cubic root of 77940 is about 42.7156284716.

Subtracting from 77940 its product of nonzero digits (1764), we obtain a square (76176 = 276²).

The spelling of 77940 in words is "seventy-seven thousand, nine hundred forty".