105352000 has 112 divisors (see below), whose sum is σ = 281251152. Its totient is φ = 38860800.

The previous prime is 105351977. The next prime is 105352003. The reversal of 105352000 is 253501.

It can be written as a sum of positive squares in 8 ways, for example, as 89415936 + 15936064 = 9456^2 + 3992^2 .

It is a super-2 number, since 2×105352000² = 22198087808000000, which contains 22 as substring.

It is a hoax number, since the sum of its digits (16) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (16).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (105352003) by changing a digit.

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 15 ways as a sum of consecutive naturals, for example, 103494 + ... + 104506.

It is an arithmetic number, because the mean of its divisors is an integer number (2511171).

Almost surely, 2^105352000 is an apocalyptic number.

105352000 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 105352000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (140625576).

105352000 is an abundant number, since it is smaller than the sum of its proper divisors (175899152).

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

105352000 is a wasteful number, since it uses less digits than its factorization.

105352000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1053 (or 1033 counting only the distinct ones).

The product of its (nonzero) digits is 150, while the sum is 16.

The square root of 105352000 is about 10264.1122363310. The cubic root of 105352000 is about 472.2959936009.

The spelling of 105352000 in words is "one hundred five million, three hundred fifty-two thousand".