1728 has 28 divisors (see below), whose sum is σ = 5080. Its totient is φ = 576.

The previous prime is 1723. The next prime is 1733. The reversal of 1728 is 8271.

The cubic root of 1728 is 12.

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

It is a Jordan-Polya number, since it can be written as 4! ⋅ (3!)^{2} ⋅ 2!.

1728 is nontrivially palindromic in base 11.

It is an interprime number because it is at equal distance from previous prime (1723) and next prime (1733).

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

It is a compositorial, being equal to the product of composites up to 9.

It is a nialpdrome in base 8 and base 12.

It is a zygodrome in base 8.

It is a self number, because there is not a number *n* which added to its sum of digits gives 1728.

It is not an unprimeable number, because it can be changed into a prime (1721) by changing a digit.

1728 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 575 + 576 + 577.

1728 is a gapful number since it is divisible by the number (18) 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 1728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2540).

1728 is an abundant number, since it is smaller than the sum of its proper divisors (3352).

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

1728 is an equidigital number, since it uses as much as digits as its factorization.

1728 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 21 (or 5 counting only the distinct ones).

The product of its digits is 112, while the sum is 18.

The square root of 1728 is about 41.5692193817.

Adding to 1728 its reverse (8271), we get a palindrome (9999).

It can be divided in two parts, 17 and 28, that added together give a triangular number (45 = T_{9}).

The spelling of 1728 in words is "one thousand, seven hundred twenty-eight".

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