72135810000 has 600 divisors, whose sum is σ = 262216170216. Its totient is φ = 18493440000.

The previous prime is 72135809989. The next prime is 72135810049. The reversal of 72135810000 is 1853127.

72135810000 is a `hidden beast` number, since 72 + 13 + 581 + 0 + 0 + 0 + 0 = 666.

It can be written as a sum of positive squares in 20 ways, for example, as 67396313664 + 4739496336 = 259608^2 + 68844^2 .

It is a tau number, because it is divible by the number of its divisors (600).

It is a super-2 number, since 2×72135810000² (a number of 23 digits) contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 416969914 + ... + 416970086.

Almost surely, 2^72135810000 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 72135810000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (131108085108).

72135810000 is an abundant number, since it is smaller than the sum of its proper divisors (190080360216).

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

72135810000 is a wasteful number, since it uses less digits than its factorization.

72135810000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 361 (or 337 counting only the distinct ones).

The product of its (nonzero) digits is 1680, while the sum is 27.

The spelling of 72135810000 in words is "seventy-two billion, one hundred thirty-five million, eight hundred ten thousand".