102564 has 72 divisors (see below), whose sum is σ = 331968. Its totient is φ = 25920.

The previous prime is 102563. The next prime is 102587. The reversal of 102564 is 465201.

It is a happy number.

102564 is a `hidden beast` number, since 102 + 564 = 666.

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

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 102564.

It is not an unprimeable number, because it can be changed into a prime (102563) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 2754 + ... + 2790.

2¹⁰²⁵⁶⁴ is an apocalyptic number.

102564 is a gapful number since it is divisible by the number (14) 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 102564, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (165984).

102564 is an abundant number, since it is smaller than the sum of its proper divisors (229404).

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

102564 is a wasteful number, since it uses less digits than its factorization.

102564 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 65 (or 60 counting only the distinct ones).

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

The square root of 102564 is about 320.2561474820. The cubic root of 102564 is about 46.8092464746.

Adding to 102564 its reverse (465201), we get a palindrome (567765).

It can be divided in two parts, 1025 and 64, that added together give a square (1089 = 33²).

The spelling of 102564 in words is "one hundred two thousand, five hundred sixty-four".