105057000 has 160 divisors (see below), whose sum is σ = 367515720. Its totient is φ = 27993600.

The previous prime is 105056999. The next prime is 105057019. The reversal of 105057000 is 750501.

It is a happy number.

It can be written as a sum of positive squares in 4 ways, for example, as 68260644 + 36796356 = 8262^2 + 6066^2 .

It is a super-2 number, since 2×105057000² = 22073946498000000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an unprimeable number.

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 39 ways as a sum of consecutive naturals, for example, 80352 + ... + 81648.

Almost surely, 2^105057000 is an apocalyptic number.

105057000 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 105057000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (183757860).

105057000 is an abundant number, since it is smaller than the sum of its proper divisors (262458720).

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

105057000 is a wasteful number, since it uses less digits than its factorization.

105057000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1330 (or 1307 counting only the distinct ones).

The product of its (nonzero) digits is 175, while the sum is 18.

The square root of 105057000 is about 10249.7317038057. The cubic root of 105057000 is about 471.8547503846.

The spelling of 105057000 in words is "one hundred five million, fifty-seven thousand".