77952 has 64 divisors (see below), whose sum is σ = 244800. Its totient is φ = 21504.

The previous prime is 77951. The next prime is 77969. The reversal of 77952 is 25977.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (64).

It is not an unprimeable number, because it can be changed into a prime (77951) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 2674 + ... + 2702.

It is an arithmetic number, because the mean of its divisors is an integer number (3825).

2⁷⁷⁹⁵² 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 77952, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (122400).

77952 is an abundant number, since it is smaller than the sum of its proper divisors (166848).

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

77952 is a wasteful number, since it uses less digits than its factorization.

77952 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 53 (or 41 counting only the distinct ones).

The product of its digits is 4410, while the sum is 30.

The square root of 77952 is about 279.1988538658. The cubic root of 77952 is about 42.7178205905.

The spelling of 77952 in words is "seventy-seven thousand, nine hundred fifty-two".