76560 has 80 divisors (see below), whose sum is σ = 267840. Its totient is φ = 17920.

The previous prime is 76543. The next prime is 76561. The reversal of 76560 is 6567.

It is a tau number, because it is divible by the number of its divisors (80).

It is a super-2 number, since 2×76560² = 11722867200, which contains 22 as substring.

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

It is a nialpdrome in base 5.

It is a self number, because there is not a number n which added to its sum of digits gives 76560.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 76560.

It is not an unprimeable number, because it can be changed into a prime (76561) by changing a digit.

76560 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 15 ways as a sum of consecutive naturals, for example, 2626 + ... + 2654.

It is an arithmetic number, because the mean of its divisors is an integer number (3348).

2⁷⁶⁵⁶⁰ 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 76560, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (133920).

76560 is an abundant number, since it is smaller than the sum of its proper divisors (191280).

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

76560 is a wasteful number, since it uses less digits than its factorization.

76560 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 56 (or 50 counting only the distinct ones).

The product of its (nonzero) digits is 1260, while the sum is 24.

The square root of 76560 is about 276.6947776883. The cubic root of 76560 is about 42.4620191243.

It can be divided in two parts, 76 and 560, that added together give a palindrome (636).

The spelling of 76560 in words is "seventy-six thousand, five hundred sixty".