72512042400 has 1080 divisors, whose sum is σ = 315679193676. Its totient is φ = 16140902400.

The previous prime is 72512042387. The next prime is 72512042417. The reversal of 72512042400 is 424021527.

72512042400 is a `hidden beast` number, since 7 + 2 + 51 + 204 + 2 + 400 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 1024256016 + 71487786384 = 32004^2 + 267372^2 .

It is a tau number, because it is divible by the number of its divisors (1080).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

It is a polite number, since it can be written in 179 ways as a sum of consecutive naturals, for example, 130182922 + ... + 130183478.

Almost surely, 2^72512042400 is an apocalyptic number.

72512042400 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 72512042400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (157839596838).

72512042400 is an abundant number, since it is smaller than the sum of its proper divisors (243167151276).

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

72512042400 is a wasteful number, since it uses less digits than its factorization.

72512042400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 644 (or 615 counting only the distinct ones).

The product of its (nonzero) digits is 4480, while the sum is 27.

Adding to 72512042400 its reverse (424021527), we get a palindrome (72936063927).

The spelling of 72512042400 in words is "seventy-two billion, five hundred twelve million, forty-two thousand, four hundred".