10749542400 has 459 divisors, whose sum is σ = 39985961041. Its totient is φ = 2866544640.

The previous prime is 10749542393. The next prime is 10749542431. The reversal of 10749542400 is 424594701.

It is a happy number.

The square root of 10749542400 is 103680.

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

It is a Jordan-Polya number, since it can be written as (6!)² ⋅ (4!)² ⋅ (3!)².

10749542400 is a `hidden beast` number, since 1 + 0 + 74 + 9 + 542 + 40 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 3869835264 + 6879707136 = 62208^2 + 82944^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a Duffinian number.

It is a nialpdrome in base 12.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 2149908478 + ... + 2149908482.

Almost surely, 2^10749542400 is an apocalyptic number.

10749542400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

10749542400 is the 103680-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 10749542400

10749542400 is an abundant number, since it is smaller than the sum of its proper divisors (29236418641).

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

10749542400 is an frugal number, since it uses more digits than its factorization.

10749542400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 66 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 40320, while the sum is 36.

Multiplying 10749542400 by its sum of digits (36), we get a square (386983526400 = 622080²).

10749542400 divided by its sum of digits (36) gives a square (298598400 = 17280²).

The spelling of 10749542400 in words is "ten billion, seven hundred forty-nine million, five hundred forty-two thousand, four hundred".