105872144400 has 1215 divisors, whose sum is σ = 444298565893. Its totient is φ = 23323238400.

The previous prime is 105872144387. The next prime is 105872144401. The reversal of 105872144400 is 4441278501.

It is a happy number.

The square root of 105872144400 is 325380.

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

105872144400 is a `hidden beast` number, since 10 + 587 + 21 + 4 + 4 + 40 + 0 = 666.

It can be written as a sum of positive squares in 13 ways, for example, as 34493404176 + 71378740224 = 185724^2 + 267168^2 .

It is a super-2 number, since 2×105872144400² (a number of 23 digits) contains 22 as substring.

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

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (105872144401) by changing a digit.

It is a polite number, since it can be written in 242 ways as a sum of consecutive naturals, for example, 3650763586 + ... + 3650763614.

Almost surely, 2^105872144400 is an apocalyptic number.

105872144400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

105872144400 is the 325380-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 105872144400

105872144400 is an abundant number, since it is smaller than the sum of its proper divisors (338426421493).

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

105872144400 is a wasteful number, since it uses less digits than its factorization.

105872144400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 138 (or 67 counting only the distinct ones).

The product of its (nonzero) digits is 35840, while the sum is 36.

Multiplying 105872144400 by its sum of digits (36), we get a square (3811397198400 = 1952280²).

105872144400 divided by its sum of digits (36) gives a square (2940892900 = 54230²).

The spelling of 105872144400 in words is "one hundred five billion, eight hundred seventy-two million, one hundred forty-four thousand, four hundred".