105638400 has 360 divisors, whose sum is σ = 435356064. Its totient is φ = 23961600.

The previous prime is 105638399. The next prime is 105638437. The reversal of 105638400 is 4836501.

It is a tau number, because it is divible by the number of its divisors (360).

It is a super-2 number, since 2×105638400² = 22318943109120000, which contains 22 as substring.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 806335 + ... + 806465.

Almost surely, 2^105638400 is an apocalyptic number.

105638400 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 105638400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (217678032).

105638400 is an abundant number, since it is smaller than the sum of its proper divisors (329717664).

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

105638400 is a wasteful number, since it uses less digits than its factorization.

105638400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 172 (or 148 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 27.

The square root of 105638400 is about 10278.0542905747. The cubic root of 105638400 is about 472.7235861287.

The spelling of 105638400 in words is "one hundred five million, six hundred thirty-eight thousand, four hundred".