105315600 has 240 divisors, whose sum is σ = 374128832. Its totient is φ = 25159680.

The previous prime is 105315583. The next prime is 105315601. The reversal of 105315600 is 6513501.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (240).

It is a super-2 number, since 2×105315600² = 22182751206720000, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (105315601) 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 47 ways as a sum of consecutive naturals, for example, 670722 + ... + 670878.

Almost surely, 2^105315600 is an apocalyptic number.

105315600 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 105315600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (187064416).

105315600 is an abundant number, since it is smaller than the sum of its proper divisors (268813232).

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

105315600 is a wasteful number, since it uses less digits than its factorization.

105315600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 234 (or 223 counting only the distinct ones).

The product of its (nonzero) digits is 450, while the sum is 21.

The square root of 105315600 is about 10262.3389146919. The cubic root of 105315600 is about 472.2415932589.

It can be divided in two parts, 1053 and 15600, that added together give a triangular number (16653 = T₁₈₂).

The spelling of 105315600 in words is "one hundred five million, three hundred fifteen thousand, six hundred".