653072000 has 320 divisors, whose sum is σ = 2005628040. Its totient is φ = 210739200.

The previous prime is 653071999. The next prime is 653072023. The reversal of 653072000 is 270356.

It can be written as a sum of positive squares in 4 ways, for example, as 284124736 + 368947264 = 16856^2 + 19208^2 .

It is a tau number, because it is divible by the number of its divisors (320).

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 39 ways as a sum of consecutive naturals, for example, 38415992 + ... + 38416008.

Almost surely, 2^653072000 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 653072000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1002814020).

653072000 is an abundant number, since it is smaller than the sum of its proper divisors (1352556040).

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

653072000 is an frugal number, since it uses more digits than its factorization.

653072000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 74 (or 31 counting only the distinct ones).

The product of its (nonzero) digits is 1260, while the sum is 23.

The square root of 653072000 is about 25555.2734283944. The cubic root of 653072000 is about 867.6016208638.

The spelling of 653072000 in words is "six hundred fifty-three million, seventy-two thousand".