72405964800 has 1440 divisors, whose sum is σ = 309664555200. Its totient is φ = 16562257920.

The previous prime is 72405964759. The next prime is 72405964801. The reversal of 72405964800 is 846950427.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (1440).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72405964801) by changing a digit.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 916531161 + ... + 916531239.

It is an arithmetic number, because the mean of its divisors is an integer number (215044830).

Almost surely, 2^72405964800 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 72405964800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (154832277600).

72405964800 is an abundant number, since it is smaller than the sum of its proper divisors (237258590400).

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

72405964800 is a wasteful number, since it uses less digits than its factorization.

72405964800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 153 (or 119 counting only the distinct ones).

The product of its (nonzero) digits is 483840, while the sum is 45.

The spelling of 72405964800 in words is "seventy-two billion, four hundred five million, nine hundred sixty-four thousand, eight hundred".