313728 has 64 divisors (see below), whose sum is σ = 897600. Its totient is φ = 96768.

The previous prime is 313727. The next prime is 313739. The reversal of 313728 is 827313.

313728 is nontrivially palindromic in base 7.

313728 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (64).

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a junction number, because it is equal to n+sod(n) for n = 313698 and 313707.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 313728.

It is not an unprimeable number, because it can be changed into a prime (313721) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 7275 + ... + 7317.

It is an arithmetic number, because the mean of its divisors is an integer number (14025).

313728 is a Friedman number, since it can be written as (8*(7^(3*2)-1))/3, using all its digits and the basic arithmetic operations.

2³¹³⁷²⁸ is an apocalyptic number.

313728 is a gapful number since it is divisible by the number (38) 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 313728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (448800).

313728 is an abundant number, since it is smaller than the sum of its proper divisors (583872).

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

313728 is a wasteful number, since it uses less digits than its factorization.

313728 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 79 (or 67 counting only the distinct ones).

The product of its digits is 1008, while the sum is 24.

The square root of 313728 is about 560.1142740549. The cubic root of 313728 is about 67.9492123657.

It can be divided in two parts, 3 and 13728, that added together give a palindrome (13731).

The spelling of 313728 in words is "three hundred thirteen thousand, seven hundred twenty-eight".