725188464000 has 3840 divisors, whose sum is σ = 3720704232960. Its totient is φ = 135862272000.

The previous prime is 725188463981. The next prime is 725188464017. The reversal of 725188464000 is 464881527.

725188464000 is a `hidden beast` number, since 7 + 2 + 5 + 188 + 464 + 0 + 0 + 0 = 666.

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

It is a congruent number.

It is an unprimeable number.

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 479 ways as a sum of consecutive naturals, for example, 16864847979 + ... + 16864848021.

It is an arithmetic number, because the mean of its divisors is an integer number (968933394).

Almost surely, 2^725188464000 is an apocalyptic number.

725188464000 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 725188464000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1860352116480).

725188464000 is an abundant number, since it is smaller than the sum of its proper divisors (2995515768960).

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

725188464000 is a wasteful number, since it uses less digits than its factorization.

725188464000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 128 (or 84 counting only the distinct ones).

The product of its (nonzero) digits is 430080, while the sum is 45.

The spelling of 725188464000 in words is "seven hundred twenty-five billion, one hundred eighty-eight million, four hundred sixty-four thousand".