72553985667072 has 1456 divisors, whose sum is σ = 269829114609600. Its totient is φ = 18985698459648.

The previous prime is 72553985667067. The next prime is 72553985667101. The reversal of 72553985667072 is 27076658935527.

72553985667072 is a `hidden beast` number, since 7 + 2 + 5 + 53 + 9 + 8 + 566 + 7 + 0 + 7 + 2 = 666.

It is a tau number, because it is divible by the number of its divisors (1456).

It is a super-3 number, since 3×72553985667072³ (a number of 43 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (72).

It is a congruent number.

It is an unprimeable number.

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 111 ways as a sum of consecutive naturals, for example, 37226261554 + ... + 37226263502.

It is an arithmetic number, because the mean of its divisors is an integer number (185322194100).

Almost surely, 2^{72553985667072} is an apocalyptic number.

72553985667072 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 72553985667072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (134914557304800).

72553985667072 is an abundant number, since it is smaller than the sum of its proper divisors (197275128942528).

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

72553985667072 is a wasteful number, since it uses less digits than its factorization.

72553985667072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2148 (or 2111 counting only the distinct ones).

The product of its (nonzero) digits is 1333584000, while the sum is 72.

The spelling of 72553985667072 in words is "seventy-two trillion, five hundred fifty-three billion, nine hundred eighty-five million, six hundred sixty-seven thousand, seventy-two".