72563904 has 168 divisors, whose sum is σ = 248442480. Its totient is φ = 20708352.

The previous prime is 72563903. The next prime is 72563921. The reversal of 72563904 is 40936527.

72563904 is a `hidden beast` number, since 7 + 2 + 563 + 90 + 4 = 666.

It is a tau number, because it is divible by the number of its divisors (168).

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

It is a zygodrome in base 6.

It is not an unprimeable number, because it can be changed into a prime (72563903) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 84244 + ... + 85100.

Almost surely, 2^72563904 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 72563904, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (124221240).

72563904 is an abundant number, since it is smaller than the sum of its proper divisors (175878576).

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

72563904 is a wasteful number, since it uses less digits than its factorization.

72563904 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 892 (or 869 counting only the distinct ones).

The product of its (nonzero) digits is 45360, while the sum is 36.

The square root of 72563904 is about 8518.4449285066. Note that the first 3 decimals coincide. The cubic root of 72563904 is about 417.1000225879.

The spelling of 72563904 in words is "seventy-two million, five hundred sixty-three thousand, nine hundred four".