10013300784400 has 405 divisors, whose sum is σ = 26309714532397. Its totient is φ = 3661567385600.

The previous prime is 10013300784287. The next prime is 10013300784407. The reversal of 10013300784400 is 448700331001.

The square root of 10013300784400 is 3164380.

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

10013300784400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 13 ways, for example, as 8670928286736 + 1342372497664 = 2944644^2 + 1158608^2 .

It is a hoax number, since the sum of its digits (31) coincides with the sum of the digits of its distinct prime factors.

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (10013300784407) by changing a digit.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 44111457087 + ... + 44111457313.

Almost surely, 2^{10013300784400} is an apocalyptic number.

10013300784400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

10013300784400 is the 3164380-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 10013300784400

10013300784400 is an abundant number, since it is smaller than the sum of its proper divisors (16296413747997).

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

10013300784400 is an equidigital number, since it uses as much as digits as its factorization.

10013300784400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 588 (or 292 counting only the distinct ones).

The product of its (nonzero) digits is 8064, while the sum is 31.

The spelling of 10013300784400 in words is "ten trillion, thirteen billion, three hundred million, seven hundred eighty-four thousand, four hundred".