1026564000 has 576 divisors, whose sum is σ = 4266452736. Its totient is φ = 211200000.

The previous prime is 1026563957. The next prime is 1026564047. The reversal of 1026564000 is 4656201.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 10163950 + ... + 10164050.

It is an arithmetic number, because the mean of its divisors is an integer number (7407036).

Almost surely, 2^1026564000 is an apocalyptic number.

1026564000 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 1026564000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2133226368).

1026564000 is an abundant number, since it is smaller than the sum of its proper divisors (3239888736).

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

1026564000 is a wasteful number, since it uses less digits than its factorization.

1026564000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 158 (or 129 counting only the distinct ones).

The product of its (nonzero) digits is 1440, while the sum is 24.

The square root of 1026564000 is about 32040.0374531616. The cubic root of 1026564000 is about 1008.7773985301. Note that the first 3 decimals are identical.

The spelling of 1026564000 in words is "one billion, twenty-six million, five hundred sixty-four thousand".