10005408000 has 648 divisors, whose sum is σ = 41939384760. Its totient is φ = 2283724800.

The previous prime is 10005407989. The next prime is 10005408013. The reversal of 10005408000 is 80450001.

It can be written as a sum of positive squares in 4 ways, for example, as 1652910336 + 8352497664 = 40656^2 + 91392^2 .

It is a Harshad number since it is a multiple of its sum of digits (18).

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 71 ways as a sum of consecutive naturals, for example, 14111646 + ... + 14112354.

Almost surely, 2^10005408000 is an apocalyptic number.

10005408000 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 10005408000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (20969692380).

10005408000 is an abundant number, since it is smaller than the sum of its proper divisors (31933976760).

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

10005408000 is an equidigital number, since it uses as much as digits as its factorization.

10005408000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 760 (or 726 counting only the distinct ones).

The product of its (nonzero) digits is 160, while the sum is 18.

Adding to 10005408000 its reverse (80450001), we get a palindrome (10085858001).

The spelling of 10005408000 in words is "ten billion, five million, four hundred eight thousand".