72505827717120 has 1456 divisors, whose sum is σ = 299862268235712. Its totient is φ = 16476898590720.

The previous prime is 72505827717079. The next prime is 72505827717121. The reversal of 72505827717120 is 2171772850527.

72505827717120 is a `hidden beast` number, since 7 + 2 + 50 + 582 + 7 + 7 + 1 + 7 + 1 + 2 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72505827717121) by changing a digit.

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 111 ways as a sum of consecutive naturals, for example, 18916206724 + ... + 18916210556.

It is an arithmetic number, because the mean of its divisors is an integer number (205949360052).

Almost surely, 2^{72505827717120} is an apocalyptic number.

72505827717120 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 72505827717120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (149931134117856).

72505827717120 is an abundant number, since it is smaller than the sum of its proper divisors (227356440518592).

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

72505827717120 is an equidigital number, since it uses as much as digits as its factorization.

72505827717120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 4068 (or 4031 counting only the distinct ones).

The product of its (nonzero) digits is 3841600, while the sum is 54.

The spelling of 72505827717120 in words is "seventy-two trillion, five hundred five billion, eight hundred twenty-seven million, seven hundred seventeen thousand, one hundred twenty".