78624 has 96 divisors (see below), whose sum is σ = 282240. Its totient is φ = 20736.

The previous prime is 78623. The next prime is 78643. The reversal of 78624 is 42687.

78624 = T₁₄ + T₁₅ + ... + T₇₇.

It is a tau number, because it is divible by the number of its divisors (96).

It is a Harshad number since it is a multiple of its sum of digits (27).

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

It is one of the 548 Lynch-Bell numbers.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (78623) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 6042 + ... + 6054.

It is an arithmetic number, because the mean of its divisors is an integer number (2940).

2⁷⁸⁶²⁴ 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 78624, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (141120).

78624 is an abundant number, since it is smaller than the sum of its proper divisors (203616).

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

78624 is a wasteful number, since it uses less digits than its factorization.

78624 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 39 (or 25 counting only the distinct ones).

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

The square root of 78624 is about 280.3997146932. The cubic root of 78624 is about 42.8402218915.

Subtracting from 78624 its reverse (42687), we obtain a cube (35937 = 33³).

The spelling of 78624 in words is "seventy-eight thousand, six hundred twenty-four".