77364 has 36 divisors (see below), whose sum is σ = 224224. Its totient is φ = 22032.

The previous prime is 77359. The next prime is 77369. The reversal of 77364 is 46377.

It is an interprime number because it is at equal distance from previous prime (77359) and next prime (77369).

It is a tau number, because it is divible by the number of its divisors (36).

It is a Smith number, since the sum of its digits (27) coincides with the sum of the digits of its prime factors.

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 77364.

It is not an unprimeable number, because it can be changed into a prime (77369) 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, 99 + ... + 405.

2⁷⁷³⁶⁴ 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 77364, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (112112).

77364 is an abundant number, since it is smaller than the sum of its proper divisors (146860).

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

77364 is a wasteful number, since it uses less digits than its factorization.

77364 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 324 (or 319 counting only the distinct ones).

The product of its digits is 3528, while the sum is 27.

The square root of 77364 is about 278.1438476760. The cubic root of 77364 is about 42.6101410757.

It can be divided in two parts, 77 and 364, that added together give a square (441 = 21²).

The spelling of 77364 in words is "seventy-seven thousand, three hundred sixty-four".