77580 has 36 divisors (see below), whose sum is σ = 235872. Its totient is φ = 20640.

The previous prime is 77573. The next prime is 77587. The reversal of 77580 is 8577.

77580 = 23² + 24² + ... + 62².

It is an interprime number because it is at equal distance from previous prime (77573) and next prime (77587).

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

It is not an unprimeable number, because it can be changed into a prime (77587) by changing a digit.

77580 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 11 ways as a sum of consecutive naturals, for example, 36 + ... + 395.

It is an arithmetic number, because the mean of its divisors is an integer number (6552).

2⁷⁷⁵⁸⁰ 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 77580, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (117936).

77580 is an abundant number, since it is smaller than the sum of its proper divisors (158292).

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

77580 is a wasteful number, since it uses less digits than its factorization.

77580 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 446 (or 441 counting only the distinct ones).

The product of its (nonzero) digits is 1960, while the sum is 27.

The square root of 77580 is about 278.5318653224. The cubic root of 77580 is about 42.6497600117.

The spelling of 77580 in words is "seventy-seven thousand, five hundred eighty".