76320 has 72 divisors (see below), whose sum is σ = 265356. Its totient is φ = 19968.

The previous prime is 76303. The next prime is 76333. The reversal of 76320 is 2367.

It can be written as a sum of positive squares in 2 ways, for example, as 76176 + 144 = 276^2 + 12^2 .

It is a tau number, because it is divible by the number of its divisors (72).

It is a super-3 number, since 3×76320³ = 1333633019904000, which contains 333 as substring.

It is a hoax number, since the sum of its digits (18) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an Ulam number.

It is a nialpdrome in base 10.

It is a junction number, because it is equal to n+sod(n) for n = 76293 and 76302.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 76320.

It is an unprimeable 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 11 ways as a sum of consecutive naturals, for example, 1414 + ... + 1466.

2⁷⁶³²⁰ 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 76320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (132678).

76320 is an abundant number, since it is smaller than the sum of its proper divisors (189036).

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

76320 is a wasteful number, since it uses less digits than its factorization.

76320 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 74 (or 63 counting only the distinct ones).

The product of its (nonzero) digits is 252, while the sum is 18.

The square root of 76320 is about 276.2607463973. The cubic root of 76320 is about 42.4176027539.

Adding to 76320 its reverse (2367), we get a palindrome (78687).

The spelling of 76320 in words is "seventy-six thousand, three hundred twenty".