105872000 has 128 divisors (see below), whose sum is σ = 284029200. Its totient is φ = 39014400.

The previous prime is 105871979. The next prime is 105872003. The reversal of 105872000 is 278501.

It can be written as a sum of positive squares in 8 ways, for example, as 2483776 + 103388224 = 1576^2 + 10168^2 .

It is a tau number, because it is divible by the number of its divisors (128).

It is a super-2 number, since 2×105872000² = 22417760768000000, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (105872003) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 207746 + ... + 208254.

Almost surely, 2^105872000 is an apocalyptic number.

105872000 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 105872000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (142014600).

105872000 is an abundant number, since it is smaller than the sum of its proper divisors (178157200).

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

105872000 is an equidigital number, since it uses as much as digits as its factorization.

105872000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 551 (or 529 counting only the distinct ones).

The product of its (nonzero) digits is 560, while the sum is 23.

The square root of 105872000 is about 10289.4120337364. The cubic root of 105872000 is about 473.0717768507.

The spelling of 105872000 in words is "one hundred five million, eight hundred seventy-two thousand".