105185664 has 192 divisors, whose sum is σ = 330810480. Its totient is φ = 31948800.

The previous prime is 105185657. The next prime is 105185683. The reversal of 105185664 is 466581501.

It is a tau number, because it is divible by the number of its divisors (192).

It is a super-2 number, since 2×105185664² = 22128047822241792, which contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 802879 + ... + 803009.

Almost surely, 2^105185664 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 105185664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (165405240).

105185664 is an abundant number, since it is smaller than the sum of its proper divisors (225624816).

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

105185664 is a wasteful number, since it uses less digits than its factorization.

105185664 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 209 (or 194 counting only the distinct ones).

The product of its (nonzero) digits is 28800, while the sum is 36.

The square root of 105185664 is about 10256.0062402477. The cubic root of 105185664 is about 472.0472996743.

The spelling of 105185664 in words is "one hundred five million, one hundred eighty-five thousand, six hundred sixty-four".