10064102400 has 891 divisors, whose sum is σ = 41802235293. Its totient is φ = 2311372800.

The previous prime is 10064102393. The next prime is 10064102423. The reversal of 10064102400 is 420146001.

The square root of 10064102400 is 100320.

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

10064102400 is a `hidden beast` number, since 1 + 0 + 0 + 641 + 0 + 24 + 0 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 3623076864 + 6441025536 = 60192^2 + 80256^2 .

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 80 ways as a sum of consecutive naturals, for example, 529689591 + ... + 529689609.

Almost surely, 2^10064102400 is an apocalyptic number.

10064102400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

10064102400 is the 100320-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 10064102400

10064102400 is an abundant number, since it is smaller than the sum of its proper divisors (31738132893).

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

10064102400 is a wasteful number, since it uses less digits than its factorization.

10064102400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 96 (or 40 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

Adding to 10064102400 its reverse (420146001), we get a palindrome (10484248401).

The spelling of 10064102400 in words is "ten billion, sixty-four million, one hundred two thousand, four hundred".