1664 has 16 divisors (see below), whose sum is σ = 3570. Its totient is φ = 768.

The previous prime is 1663. The next prime is 1667. The reversal of 1664 is 4661.

1664 is an esthetic number in base 7, because in such base its adjacent digits differ by 1.

It can be written as a sum of positive squares in only one way, i.e., 1600 + 64 = 40^2 + 8^2 .

It is a tau number, because it is divible by the number of its divisors (16).

It is a plaindrome in base 9.

It is a nialpdrome in base 8.

It is not an unprimeable number, because it can be changed into a prime (1663) by changing a digit.

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 as a sum of consecutive naturals, namely, 122 + ... + 134.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1785).

1664 is an abundant number, since it is smaller than the sum of its proper divisors (1906).

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

1664 is an equidigital number, since it uses as much as digits as its factorization.

1664 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 27 (or 15 counting only the distinct ones).

The product of its digits is 144, while the sum is 17.

The square root of 1664 is about 40.7921561087. The cubic root of 1664 is about 11.8499842736.

Adding to 1664 its sum of digits (17), we get a square (1681 = 41²).

It can be divided in two parts, 16 and 64, that multiplied together give a 10-th power (1024 = 2¹⁰).

The spelling of 1664 in words is "one thousand, six hundred sixty-four".