72813312 has 324 divisors, whose sum is σ = 262584504. Its totient is φ = 19169280.

The previous prime is 72813283. The next prime is 72813313. The reversal of 72813312 is 21331827.

It is not an unprimeable number, because it can be changed into a prime (72813313) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 4283128 + ... + 4283144.

It is an arithmetic number, because the mean of its divisors is an integer number (810446).

Almost surely, 2^72813312 is an apocalyptic number.

72813312 is a gapful number since it is divisible by the number (72) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72813312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (131292252).

72813312 is an abundant number, since it is smaller than the sum of its proper divisors (189771192).

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

72813312 is a wasteful number, since it uses less digits than its factorization.

72813312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 76 (or 46 counting only the distinct ones).

The product of its digits is 2016, while the sum is 27.

The square root of 72813312 is about 8533.0716626547. The cubic root of 72813312 is about 417.5773449638.

The spelling of 72813312 in words is "seventy-two million, eight hundred thirteen thousand, three hundred twelve".