313200 has 120 divisors (see below), whose sum is σ = 1153200. Its totient is φ = 80640.

The previous prime is 313163. The next prime is 313207. The reversal of 313200 is 2313.

313200 = 83² + 84² + ... + 114².

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (120).

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (313207) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 10786 + ... + 10814.

It is an arithmetic number, because the mean of its divisors is an integer number (9610).

2³¹³²⁰⁰ is an apocalyptic number.

313200 is a gapful number since it is divisible by the number (30) 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 313200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (576600).

313200 is an abundant number, since it is smaller than the sum of its proper divisors (840000).

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

313200 is a wasteful number, since it uses less digits than its factorization.

313200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 56 (or 39 counting only the distinct ones).

The product of its (nonzero) digits is 18, while the sum is 9.

The square root of 313200 is about 559.6427431853. The cubic root of 313200 is about 67.9110717578.

Adding to 313200 its reverse (2313), we get a palindrome (315513).

It can be divided in two parts, 3 and 13200, that added together give a triangular number (13203 = T₁₆₂).

The spelling of 313200 in words is "three hundred thirteen thousand, two hundred".