72624 has 40 divisors (see below), whose sum is σ = 200880. Its totient is φ = 22528.

The previous prime is 72623. The next prime is 72643. The reversal of 72624 is 42627.

It is a happy number.

It is a self number, because there is not a number n which added to its sum of digits gives 72624.

It is not an unprimeable number, because it can be changed into a prime (72623) 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, 772 + ... + 860.

It is an arithmetic number, because the mean of its divisors is an integer number (5022).

2⁷²⁶²⁴ 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 72624, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (100440).

72624 is an abundant number, since it is smaller than the sum of its proper divisors (128256).

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

72624 is a wasteful number, since it uses less digits than its factorization.

72624 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 117 (or 111 counting only the distinct ones).

The product of its digits is 672, while the sum is 21.

The square root of 72624 is about 269.4884042032. The cubic root of 72624 is about 41.7215135498.

It can be divided in two parts, 726 and 24, that multiplied together give a square (17424 = 132²).

The spelling of 72624 in words is "seventy-two thousand, six hundred twenty-four".