10164491712400 has 135 divisors (see below), whose sum is σ = 25943938877689. Its totient is φ = 3826224087040.

The previous prime is 10164491712337. The next prime is 10164491712407. The reversal of 10164491712400 is 421719446101.

The square root of 10164491712400 is 3188180.

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

It can be written as a sum of positive squares in 13 ways, for example, as 7904352315024 + 2260139397376 = 2811468^2 + 1503376^2 .

It is a Harshad number since it is a multiple of its sum of digits (40).

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (10164491712407) by changing a digit.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 1083976512 + ... + 1083985888.

Almost surely, 2^{10164491712400} is an apocalyptic number.

10164491712400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

10164491712400 is the 3188180-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 10164491712400

10164491712400 is an abundant number, since it is smaller than the sum of its proper divisors (15779447165289).

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

10164491712400 is an frugal number, since it uses more digits than its factorization.

10164491712400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 18806 (or 9401 counting only the distinct ones).

The product of its (nonzero) digits is 48384, while the sum is 40.

The spelling of 10164491712400 in words is "ten trillion, one hundred sixty-four billion, four hundred ninety-one million, seven hundred twelve thousand, four hundred".