72577668800 has 336 divisors, whose sum is σ = 220457889792. Its totient is φ = 22900838400.

The previous prime is 72577668799. The next prime is 72577668803. The reversal of 72577668800 is 886677527.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (56).

It is not an unprimeable number, because it can be changed into a prime (72577668803) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 73236305 + ... + 73237295.

It is an arithmetic number, because the mean of its divisors is an integer number (656124672).

Almost surely, 2^72577668800 is an apocalyptic number.

72577668800 is a gapful number since it is divisible by the number (70) 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 72577668800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (110228944896).

72577668800 is an abundant number, since it is smaller than the sum of its proper divisors (147880220992).

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

72577668800 is a wasteful number, since it uses less digits than its factorization.

72577668800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1536 (or 1521 counting only the distinct ones).

The product of its (nonzero) digits is 7902720, while the sum is 56.

The spelling of 72577668800 in words is "seventy-two billion, five hundred seventy-seven million, six hundred sixty-eight thousand, eight hundred".