2002564614400 has 675 divisors, whose sum is σ = 6103669746601. Its totient is φ = 650457077760.

The previous prime is 2002564614389. The next prime is 2002564614431. The reversal of 2002564614400 is 44164652002.

The square root of 2002564614400 is 1415120.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 720923261184 + 1281641353216 = 849072^2 + 1132096^2 .

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 74 ways as a sum of consecutive naturals, for example, 105398137591 + ... + 105398137609.

Almost surely, 2^{2002564614400} is an apocalyptic number.

2002564614400 is a gapful number since it is divisible by the number (20) formed by its first and last digit.

2002564614400 is the 1415120-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 2002564614400

2002564614400 is an abundant number, since it is smaller than the sum of its proper divisors (4101105132201).

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

2002564614400 is an frugal number, since it uses more digits than its factorization.

2002564614400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 130 (or 33 counting only the distinct ones).

The product of its (nonzero) digits is 46080, while the sum is 34.

The spelling of 2002564614400 in words is "two trillion, two billion, five hundred sixty-four million, six hundred fourteen thousand, four hundred".