10128972672 has 768 divisors, whose sum is σ = 38679379200. Its totient is φ = 2584866816.

The previous prime is 10128972671. The next prime is 10128972701. The reversal of 10128972672 is 27627982101.

It is a happy number.

10128972672 is a `hidden beast` number, since 101 + 289 + 7 + 267 + 2 = 666.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (10128972671) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 94663243 + ... + 94663349.

It is an arithmetic number, because the mean of its divisors is an integer number (50363775).

Almost surely, 2^10128972672 is an apocalyptic number.

10128972672 is a gapful number since it is divisible by the number (12) 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 10128972672, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (19339689600).

10128972672 is an abundant number, since it is smaller than the sum of its proper divisors (28550406528).

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

10128972672 is a wasteful number, since it uses less digits than its factorization.

10128972672 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 200 (or 175 counting only the distinct ones).

The product of its (nonzero) digits is 169344, while the sum is 45.

The spelling of 10128972672 in words is "ten billion, one hundred twenty-eight million, nine hundred seventy-two thousand, six hundred seventy-two".