10128409600 has 297 divisors, whose sum is σ = 27410187693. Its totient is φ = 3709992960.

The previous prime is 10128409537. The next prime is 10128409607. The reversal of 10128409600 is 690482101.

It is a happy number.

The square root of 10128409600 is 100640.

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

It can be written as a sum of positive squares in 13 ways, for example, as 313148416 + 9815261184 = 17696^2 + 99072^2 .

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (10128409607) by changing a digit.

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 26 ways as a sum of consecutive naturals, for example, 273740782 + ... + 273740818.

Almost surely, 2^10128409600 is an apocalyptic number.

10128409600 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

10128409600 is the 100640-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 10128409600

10128409600 is an abundant number, since it is smaller than the sum of its proper divisors (17281778093).

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

10128409600 is an equidigital number, since it uses as much as digits as its factorization.

10128409600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 138 (or 61 counting only the distinct ones).

The product of its (nonzero) digits is 3456, while the sum is 31.

The spelling of 10128409600 in words is "ten billion, one hundred twenty-eight million, four hundred nine thousand, six hundred".