72805824 has 224 divisors, whose sum is σ = 263997440. Its totient is φ = 19160064.

The previous prime is 72805819. The next prime is 72805829. The reversal of 72805824 is 42850827.

It is a happy number.

72805824 is a `hidden beast` number, since 72 + 8 + 0 + 582 + 4 = 666.

It is an interprime number because it is at equal distance from previous prime (72805819) and next prime (72805829).

It is a tau number, because it is divible by the number of its divisors (224).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72805829) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 157017 + ... + 157479.

It is an arithmetic number, because the mean of its divisors is an integer number (1178560).

Almost surely, 2^72805824 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 72805824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (131998720).

72805824 is an abundant number, since it is smaller than the sum of its proper divisors (191191616).

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

72805824 is a wasteful number, since it uses less digits than its factorization.

72805824 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 504 (or 488 counting only the distinct ones).

The product of its (nonzero) digits is 35840, while the sum is 36.

The square root of 72805824 is about 8532.6328879192. The cubic root of 72805824 is about 417.5630301530.

The spelling of 72805824 in words is "seventy-two million, eight hundred five thousand, eight hundred twenty-four".