105806400 has 336 divisors, whose sum is σ = 411211776. Its totient is φ = 23316480.

The previous prime is 105806399. The next prime is 105806423. The reversal of 105806400 is 4608501.

105806400 = T₄₅₁ + T₄₅₂ + ... + T₈₉₈.

It is a tau number, because it is divible by the number of its divisors (336).

It is a super-2 number, since 2×105806400² = 22389988561920000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1579167 + ... + 1579233.

Almost surely, 2^105806400 is an apocalyptic number.

105806400 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 105806400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (205605888).

105806400 is an abundant number, since it is smaller than the sum of its proper divisors (305405376).

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

105806400 is a wasteful number, since it uses less digits than its factorization.

105806400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 146 (or 131 counting only the distinct ones).

The product of its (nonzero) digits is 960, while the sum is 24.

The square root of 105806400 is about 10286.2237969043. The cubic root of 105806400 is about 472.9740490272.

105806400 divided by its product of nonzero digits (960) gives a triangular number (110215 = T₄₆₉).

The spelling of 105806400 in words is "one hundred five million, eight hundred six thousand, four hundred".