10610133582400 has 315 divisors, whose sum is σ = 28760872852155. Its totient is φ = 3852497510400.

The previous prime is 10610133582379. The next prime is 10610133582487. The reversal of 10610133582400 is 428533101601.

The square root of 10610133582400 is 3257320.

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

It can be written as a sum of positive squares in 4 ways, for example, as 1038980644416 + 9571152937984 = 1019304^2 + 3093728^2 .

It is a super-2 number, since 2×10610133582400² (a number of 27 digits) contains 22 as substring.

It is an unprimeable number.

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 44 ways as a sum of consecutive naturals, for example, 15765428464 + ... + 15765429136.

Almost surely, 2^{10610133582400} is an apocalyptic number.

10610133582400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

10610133582400 is the 3257320-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 10610133582400

10610133582400 is an abundant number, since it is smaller than the sum of its proper divisors (18150739269755).

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

10610133582400 is an frugal number, since it uses more digits than its factorization.

10610133582400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1412 (or 691 counting only the distinct ones).

The product of its (nonzero) digits is 17280, while the sum is 34.

The spelling of 10610133582400 in words is "ten trillion, six hundred ten billion, one hundred thirty-three million, five hundred eighty-two thousand, four hundred".