643968000 has 528 divisors, whose sum is σ = 2557210656. Its totient is φ = 154828800.

The previous prime is 643967993. The next prime is 643968001. The reversal of 643968000 is 869346.

643968000 is a `hidden beast` number, since 643 + 9 + 6 + 8 + 0 + 0 + 0 = 666.

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

It is not an unprimeable number, because it can be changed into a prime (643968001) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 14975979 + ... + 14976021.

It is an arithmetic number, because the mean of its divisors is an integer number (4843202).

Almost surely, 2^643968000 is an apocalyptic number.

643968000 is a gapful number since it is divisible by the number (60) 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 643968000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1278605328).

643968000 is an abundant number, since it is smaller than the sum of its proper divisors (1913242656).

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

643968000 is a wasteful number, since it uses less digits than its factorization.

643968000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 97 (or 66 counting only the distinct ones).

The product of its (nonzero) digits is 31104, while the sum is 36.

The square root of 643968000 is about 25376.5245847417. The cubic root of 643968000 is about 863.5512072504.

It can be divided in two parts, 64 and 3968000, that added together give a square (3968064 = 1992²).

The spelling of 643968000 in words is "six hundred forty-three million, nine hundred sixty-eight thousand".