76824 has 48 divisors (see below), whose sum is σ = 229320. Its totient is φ = 23040.

The previous prime is 76819. The next prime is 76829. The reversal of 76824 is 42867.

76824 is nontrivially palindromic in base 5.

It is an interprime number because it is at equal distance from previous prime (76819) and next prime (76829).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (76829) by changing a digit.

76824 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, 744 + ... + 840.

2⁷⁶⁸²⁴ 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 76824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (114660).

76824 is an abundant number, since it is smaller than the sum of its proper divisors (152496).

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

76824 is a wasteful number, since it uses less digits than its factorization.

76824 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 120 (or 113 counting only the distinct ones).

The product of its digits is 2688, while the sum is 27.

The square root of 76824 is about 277.1714270988. The cubic root of 76824 is about 42.5107700502.

It can be divided in two parts, 76 and 824, that added together give a square (900 = 30²).

The spelling of 76824 in words is "seventy-six thousand, eight hundred twenty-four".