77960 has 16 divisors (see below), whose sum is σ = 175500. Its totient is φ = 31168.

The previous prime is 77951. The next prime is 77969. The reversal of 77960 is 6977.

It is an interprime number because it is at equal distance from previous prime (77951) and next prime (77969).

It can be written as a sum of positive squares in 2 ways, for example, as 77284 + 676 = 278^2 + 26^2 .

It is a nialpdrome in base 5.

It is not an unprimeable number, because it can be changed into a prime (77969) by changing a digit.

77960 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 935 + ... + 1014.

2⁷⁷⁹⁶⁰ is an apocalyptic number.

It is an amenable number.

77960 is an abundant number, since it is smaller than the sum of its proper divisors (97540).

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 (87750).

77960 is a wasteful number, since it uses less digits than its factorization.

77960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1960 (or 1956 counting only the distinct ones).

The product of its (nonzero) digits is 2646, while the sum is 29.

The square root of 77960 is about 279.2131802047. The cubic root of 77960 is about 42.7192818781.

It can be divided in two parts, 77 and 960, that multiplied together give a triangular number (73920 = T₃₈₄).

The spelling of 77960 in words is "seventy-seven thousand, nine hundred sixty".