77352 has 32 divisors (see below), whose sum is σ = 211680. Its totient is φ = 23360.

The previous prime is 77351. The next prime is 77359. The reversal of 77352 is 25377.

77352 is nontrivially palindromic in base 13.

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

77352 is an undulating number in base 13.

It is not an unprimeable number, because it can be changed into a prime (77351) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 118 + ... + 410.

It is an arithmetic number, because the mean of its divisors is an integer number (6615).

2⁷⁷³⁵² 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 77352, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (105840).

77352 is an abundant number, since it is smaller than the sum of its proper divisors (134328).

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

77352 is a wasteful number, since it uses less digits than its factorization.

77352 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 313 (or 309 counting only the distinct ones).

The product of its digits is 1470, while the sum is 24.

The square root of 77352 is about 278.1222752676. The cubic root of 77352 is about 42.6079378626.

77352 divided by its sum of digits (24) gives a palindrome (3223).

The spelling of 77352 in words is "seventy-seven thousand, three hundred fifty-two".