77832 has 48 divisors (see below), whose sum is σ = 224640. Its totient is φ = 24288.

The previous prime is 77813. The next prime is 77839. The reversal of 77832 is 23877.

It is an Ulam number.

It is a junction number, because it is equal to n+sod(n) for n = 77796 and 77805.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 77832.

It is not an unprimeable number, because it can be changed into a prime (77839) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1633 + ... + 1679.

It is an arithmetic number, because the mean of its divisors is an integer number (4680).

2⁷⁷⁸³² is an apocalyptic number.

77832 is a gapful number since it is divisible by the number (72) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 77832, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (112320).

77832 is an abundant number, since it is smaller than the sum of its proper divisors (146808).

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

77832 is a wasteful number, since it uses less digits than its factorization.

77832 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 82 (or 75 counting only the distinct ones).

The product of its digits is 2352, while the sum is 27.

The square root of 77832 is about 278.9838705015. The cubic root of 77832 is about 42.6958892689.

It can be divided in two parts, 77 and 832, that added together give a palindrome (909).

The spelling of 77832 in words is "seventy-seven thousand, eight hundred thirty-two".