5184 has 35 divisors (see below), whose sum is σ = 15367. Its totient is φ = 1728.

The previous prime is 5179. The next prime is 5189. The reversal of 5184 is 4815.

Adding to 5184 its reverse (4815), we get a palindrome (9999).

5184 = T_{71} + T_{72}.

The square root of 5184 is 72.

It is a perfect power (a square), and thus also a powerful number.

It is a Jordan-Polya number, since it can be written as 4! ⋅ (3!)^{3}.

5184 is nontrivially palindromic in base 11.

It is an interprime number because it is at equal distance from previous prime (5179) and next prime (5189).

It is an ABA number since it can be written as A⋅B^{A}, here for A=4, B=6.

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

It is an Ulam number.

It is a Duffinian number.

Its product of digits (160) is a multiple of the sum of its prime divisors (5).

It is a plaindrome in base 13.

It is a nialpdrome in base 6, base 9 and base 12.

It is not an unprimeable number, because it can be changed into a prime (5189) by changing a digit.

5184 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 (3) of ones.

It is a polite number, since it can be written in 4 ways as a sum of consecutive naturals, for example, 1727 + 1728 + 1729.

2^{5184} is an apocalyptic number.

5184 is a gapful number since it is divisible by the number (54) formed by its first and last digit.

5184 is a droll number since its even prime factors and its odd prime factors have the same sum.

5184 is the 72-nd square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 5184

5184 is an abundant number, since it is smaller than the sum of its proper divisors (10183).

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

5184 is an equidigital number, since it uses as much as digits as its factorization.

5184 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 24 (or 5 counting only the distinct ones).

The product of its digits is 160, while the sum is 18.

The cubic root of 5184 is about 17.3069948437.

The spelling of 5184 in words is "five thousand, one hundred eighty-four".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 144 162 192 216 288 324 432 576 648 864 1296 1728 2592 5184

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