973728000 has 864 divisors, whose sum is σ = 4362059520. Its totient is φ = 212889600.

The previous prime is 973727987. The next prime is 973728043. The reversal of 973728000 is 827379.

It is a tau number, because it is divible by the number of its divisors (864).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 42335989 + ... + 42336011.

It is an arithmetic number, because the mean of its divisors is an integer number (5048680).

Almost surely, 2^973728000 is an apocalyptic number.

973728000 is a gapful number since it is divisible by the number (90) 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 973728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2181029760).

973728000 is an abundant number, since it is smaller than the sum of its proper divisors (3388331520).

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

973728000 is a wasteful number, since it uses less digits than its factorization.

973728000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 77 (or 40 counting only the distinct ones).

The product of its (nonzero) digits is 21168, while the sum is 36.

The square root of 973728000 is about 31204.6150432913. The cubic root of 973728000 is about 991.1648364429.

The spelling of 973728000 in words is "nine hundred seventy-three million, seven hundred twenty-eight thousand".