• 504 can be written using four 4's:

504 has 24 divisors (see below), whose sum is σ = 1560. Its totient is φ = 144.

The previous prime is 503. The next prime is 509. The reversal of 504 is 405.

504 = T_{7} + T_{8} + ... +
T_{14}.

504 is nontrivially palindromic in base 5.

It is a tau number, because it is divible by the number of its divisors (24).

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

It is a tribonacci number.

It is a plaindrome in base 15.

It is a nialpdrome in base 2, base 6, base 8 and base 9.

It is a zygodrome in base 2 and base 6.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (503) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 69 + ... + 75.

It is an arithmetic number, because the mean of its divisors is an integer number (65).

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 504, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (780).

504 is an abundant number, since it is smaller than the sum of its proper divisors (1056).

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

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

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

The sum of its prime factors is 19 (or 12 counting only the distinct ones).

The product of its (nonzero) digits is 20, while the sum is 9.

The square root of 504 is about 22.4499443206. The cubic root of 504 is about 7.9581144158.

Subtracting from 504 its product of nonzero digits (20), we obtain a palindrome (484).

Adding to 504 its reverse (405), we get a palindrome (909).

Subtracting from 504 its reverse (405), we obtain a palindrome (99).

The spelling of 504 in words is "five hundred four", and thus it is an aban number.

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