• 564 can be written using four 4's:

See also 113.

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564 has 12 divisors (see below), whose sum is σ = 1344. Its totient is φ = 184.

The previous prime is 563. The next prime is 569. The reversal of 564 is 465.

564 is nontrivially palindromic in base 5 and base 9.

564 is an esthetic number in base 13 and base 16, because in such bases its adjacent digits differ by 1.

It is a tau number, because it is divible by the number of its divisors (12).

564 is an undulating number in base 9.

It is a plaindrome in base 13, base 15 and base 16.

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 564.

It is not an unprimeable number, because it can be changed into a prime (563) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 12 + ... + 35.

It is an arithmetic number, because the mean of its divisors is an integer number (112).

2⁵⁶⁴ is an apocalyptic number.

It is an amenable number.

564 is an abundant number, since it is smaller than the sum of its proper divisors (780).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (672).

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

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

The sum of its prime factors is 54 (or 52 counting only the distinct ones).

The product of its digits is 120, while the sum is 15.

The square root of 564 is about 23.7486841741. The cubic root of 564 is about 8.2621492257.

Subtracting from 564 its product of digits (120), we obtain a palindrome (444).

Subtracting from 564 its reverse (465), we obtain a palindrome (99).

The spelling of 564 in words is "five hundred sixty-four", and thus it is an aban number.