1003968000 has 640 divisors, whose sum is σ = 4289725440. Its totient is φ = 226713600.

The previous prime is 1003967989. The next prime is 1003968001. The reversal of 1003968000 is 8693001.

1003968000 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (640).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (1003968001) by changing a digit.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 12095959 + ... + 12096041.

It is an arithmetic number, because the mean of its divisors is an integer number (6702696).

Almost surely, 2^1003968000 is an apocalyptic number.

1003968000 is a gapful number since it is divisible by the number (10) 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 1003968000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2144862720).

1003968000 is an abundant number, since it is smaller than the sum of its proper divisors (3285757440).

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

1003968000 is an frugal number, since it uses more digits than its factorization.

1003968000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 132 (or 100 counting only the distinct ones).

The product of its (nonzero) digits is 1296, while the sum is 27.

The square root of 1003968000 is about 31685.4540759636. The cubic root of 1003968000 is about 1001.3209210659.

The spelling of 1003968000 in words is "one billion, three million, nine hundred sixty-eight thousand".