105210 has 48 divisors (see below), whose sum is σ = 314496. Its totient is φ = 23904.

The previous prime is 105199. The next prime is 105211. The reversal of 105210 is 12501.

Adding to 105210 its reverse (12501), we get a palindrome (117711).

It is a happy number.

It is a super-2 number, since 2×105210^{2} = 22138288200, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (9).

It is an alternating number because its digits alternate between odd and even.

It is a Curzon number.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 105192 and 105201.

It is not an unprimeable number, because it can be changed into a prime (105211) by changing a digit.

105210 is an untouchable number, because it is not equal to the sum of proper divisors of any 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 23 ways as a sum of consecutive naturals, for example, 547 + ... + 713.

It is an arithmetic number, because the mean of its divisors is an integer number (6552).

105210 is a Friedman number, since it can be written as 501*210, using all its digits and the basic arithmetic operations.

It is a vampire number, since it can be written as 210 ⋅ 501 (with its own digits).

2^{105210} is an apocalyptic number.

105210 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is a practical number, because each smaller number is the sum of distinct divisors of 105210, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (157248).

105210 is an abundant number, since it is smaller than the sum of its proper divisors (209286).

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

105210 is a wasteful number, since it uses less digits than its factorization.

105210 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 187 (or 184 counting only the distinct ones).

The product of its (nonzero) digits is 10, while the sum is 9.

The square root of 105210 is about 324.3609100986. The cubic root of 105210 is about 47.2083701521.

The spelling of 105210 in words is "one hundred five thousand, two hundred ten".

Divisors: 1 2 3 5 6 7 9 10 14 15 18 21 30 35 42 45 63 70 90 105 126 167 210 315 334 501 630 835 1002 1169 1503 1670 2338 2505 3006 3507 5010 5845 7014 7515 10521 11690 15030 17535 21042 35070 52605 105210

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