10584294400 has 99 divisors (see below), whose sum is σ = 26277099501. Its totient is φ = 4227133440.

The previous prime is 10584294379. The next prime is 10584294437. The reversal of 10584294400 is 449248501.

The square root of 10584294400 is 102880.

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

It can be written as a sum of positive squares in only one way, i.e., 3810345984 + 6773948416 = 61728^2 + 82304^2 .

It is a super-2 number, since 2×10584294400² (a number of 21 digits) contains 22 as substring.

It is a Duffinian number.

It is a self number, because there is not a number n which added to its sum of digits gives 10584294400.

It is an unprimeable number.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 16460479 + ... + 16461121.

Almost surely, 2^10584294400 is an apocalyptic number.

10584294400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

10584294400 is the 102880-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 10584294400

10584294400 is an abundant number, since it is smaller than the sum of its proper divisors (15692805101).

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

10584294400 is an frugal number, since it uses more digits than its factorization.

10584294400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1316 (or 650 counting only the distinct ones).

The product of its (nonzero) digits is 46080, while the sum is 37.

The spelling of 10584294400 in words is "ten billion, five hundred eighty-four million, two hundred ninety-four thousand, four hundred".