10144097600400 has 405 divisors, whose sum is σ = 35601865371891. Its totient is φ = 2674771683840.

The previous prime is 10144097600389. The next prime is 10144097600423. The reversal of 10144097600400 is 400679044101.

The square root of 10144097600400 is 3184980.

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

10144097600400 is a `hidden beast` number, since 1 + 0 + 1 + 4 + 4 + 0 + 9 + 7 + 600 + 40 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 37191893904 + 10106905706496 = 192852^2 + 3179136^2 .

It is a super-2 number, since 2×10144097600400² (a number of 27 digits) contains 22 as substring.

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

It is an unprimeable number.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 20829768957 + ... + 20829769443.

Almost surely, 2^{10144097600400} is an apocalyptic number.

10144097600400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

10144097600400 is the 3184980-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 10144097600400

10144097600400 is an abundant number, since it is smaller than the sum of its proper divisors (25457767771491).

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

10144097600400 is an equidigital number, since it uses as much as digits as its factorization.

10144097600400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1216 (or 606 counting only the distinct ones).

The product of its (nonzero) digits is 24192, while the sum is 36.

Multiplying 10144097600400 by its sum of digits (36), we get a square (365187513614400 = 19109880²).

10144097600400 divided by its sum of digits (36) gives a square (281780488900 = 530830²).

The spelling of 10144097600400 in words is "ten trillion, one hundred forty-four billion, ninety-seven million, six hundred thousand, four hundred".