72776721712464 has 1440 divisors, whose sum is σ = 269754022137600. Its totient is φ = 17772395397120.

The previous prime is 72776721712459. The next prime is 72776721712477. The reversal of 72776721712464 is 46421712767727.

72776721712464 is a `hidden beast` number, since 7 + 27 + 7 + 67 + 21 + 71 + 2 + 464 = 666.

It is a hoax number, since the sum of its digits (63) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (63).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 177938194692 + ... + 177938195100.

It is an arithmetic number, because the mean of its divisors is an integer number (187329182040).

Almost surely, 2^{72776721712464} 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 72776721712464, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (134877011068800).

72776721712464 is an abundant number, since it is smaller than the sum of its proper divisors (196977300425136).

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

72776721712464 is a wasteful number, since it uses less digits than its factorization.

72776721712464 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 773 (or 711 counting only the distinct ones).

The product of its digits is 77446656, while the sum is 63.

The spelling of 72776721712464 in words is "seventy-two trillion, seven hundred seventy-six billion, seven hundred twenty-one million, seven hundred twelve thousand, four hundred sixty-four".