451728000 has 192 divisors, whose sum is σ = 1622785320. Its totient is φ = 120422400.

The previous prime is 451727989. The next prime is 451728047. The reversal of 451728000 is 827154.

It can be written as a sum of positive squares in 4 ways, for example, as 297769536 + 153958464 = 17256^2 + 12408^2 .

It is a tau number, because it is divible by the number of its divisors (192).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 142432 + ... + 145568.

Almost surely, 2^451728000 is an apocalyptic number.

451728000 is a gapful number since it is divisible by the number (40) 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 451728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (811392660).

451728000 is an abundant number, since it is smaller than the sum of its proper divisors (1171057320).

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

451728000 is a wasteful number, since it uses less digits than its factorization.

451728000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3172 (or 3147 counting only the distinct ones).

The product of its (nonzero) digits is 2240, while the sum is 27.

The square root of 451728000 is about 21253.8937609088. The cubic root of 451728000 is about 767.2890556173.

The spelling of 451728000 in words is "four hundred fifty-one million, seven hundred twenty-eight thousand".