105185408 has 32 divisors (see below), whose sum is σ = 212438460. Its totient is φ = 51867648.

The previous prime is 105185401. The next prime is 105185441. The reversal of 105185408 is 804581501.

It can be written as a sum of positive squares in 2 ways, for example, as 99840064 + 5345344 = 9992^2 + 2312^2 .

It is a tau number, because it is divible by the number of its divisors (32).

It is a super-2 number, since 2×105185408² = 22127940112252928, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (32).

It is not an unprimeable number, because it can be changed into a prime (105185401) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 3716 + ... + 14972.

Almost surely, 2^105185408 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 105185408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (106219230).

105185408 is an abundant number, since it is smaller than the sum of its proper divisors (107253052).

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

105185408 is an equidigital number, since it uses as much as digits as its factorization.

105185408 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 11344 (or 11332 counting only the distinct ones).

The product of its (nonzero) digits is 6400, while the sum is 32.

The square root of 105185408 is about 10255.9937597485. The cubic root of 105185408 is about 472.0469167191.

It can be divided in two parts, 105185 and 408, that multiplied together give a triangular number (42915480 = T₉₂₆₄).

The spelling of 105185408 in words is "one hundred five million, one hundred eighty-five thousand, four hundred eight".