105264 has 60 divisors (see below), whose sum is σ = 319176. Its totient is φ = 32256.

The previous prime is 105263. The next prime is 105269. The reversal of 105264 is 462501.

Adding to 105264 its reverse (462501), we get a palindrome (567765).

It is a happy number.

It is a super-2 number, since 2×105264^{2} = 22161019392, which contains 22 as substring.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (105263) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 2427 + ... + 2469.

105264 is a Friedman number, since it can be written as 516*204, using all its digits and the basic arithmetic operations.

It is a vampire number, since it can be written as 204 ⋅ 516 (with its own digits).

2^{105264} is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 105264, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (159588).

105264 is an abundant number, since it is smaller than the sum of its proper divisors (213912).

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

105264 is a wasteful number, since it uses less digits than its factorization.

105264 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 74 (or 65 counting only the distinct ones).

The product of its (nonzero) digits is 240, while the sum is 18.

The square root of 105264 is about 324.4441400303. Note that the first 3 decimals coincide. The cubic root of 105264 is about 47.2164454807.

The spelling of 105264 in words is "one hundred five thousand, two hundred sixty-four".

Divisors: 1 2 3 4 6 8 9 12 16 17 18 24 34 36 43 48 51 68 72 86 102 129 136 144 153 172 204 258 272 306 344 387 408 516 612 688 731 774 816 1032 1224 1462 1548 2064 2193 2448 2924 3096 4386 5848 6192 6579 8772 11696 13158 17544 26316 35088 52632 105264

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