16464 has 40 divisors (see below), whose sum is σ = 49600. Its totient is φ = 4704.

The previous prime is 16453. The next prime is 16477. The reversal of 16464 is 46461.

16464 is an esthetic number in base 13, because in such base its adjacent digits differ by 1.

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a nude number because it is divisible by every one of its digits.

Its product of digits (576) is a multiple of the sum of its prime divisors (12).

It is a nialpdrome in base 7, base 12 and base 14.

It is a zygodrome in base 7.

It is a self number, because there is not a number *n* which added to its sum of digits gives 16464.

It is a congruent number.

It is an unprimeable number.

16464 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 7 ways as a sum of consecutive naturals, for example, 2349 + ... + 2355.

It is an arithmetic number, because the mean of its divisors is an integer number (1240).

2^{16464} is an apocalyptic number.

16464 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 16464, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (24800).

16464 is an abundant number, since it is smaller than the sum of its proper divisors (33136).

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

16464 is an equidigital number, since it uses as much as digits as its factorization.

16464 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 32 (or 12 counting only the distinct ones).

The product of its digits is 576, while the sum is 21.

The square root of 16464 is about 128.3121194588. The cubic root of 16464 is about 25.4396882996.

Multiplying 16464 by its sum of digits (21), we get a square (345744 = 588^{2}).

16464 divided by its sum of digits (21) gives a square (784 = 28^{2}).

The spelling of 16464 in words is "sixteen thousand, four hundred sixty-four".

Divisors: 1 2 3 4 6 7 8 12 14 16 21 24 28 42 48 49 56 84 98 112 147 168 196 294 336 343 392 588 686 784 1029 1176 1372 2058 2352 2744 4116 5488 8232 16464

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