313344000 has 360 divisors, whose sum is σ = 1196126568. Its totient is φ = 78643200.

The previous prime is 313343999. The next prime is 313344013. The reversal of 313344000 is 443313.

It can be written as a sum of positive squares in 4 ways, for example, as 1327104 + 312016896 = 1152^2 + 17664^2 .

It is a tau number, because it is divible by the number of its divisors (360).

It is a hoax number, since the sum of its digits (18) coincides with the sum of the digits of its distinct prime factors.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 18431992 + ... + 18432008.

Almost surely, 2^313344000 is an apocalyptic number.

313344000 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 313344000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (598063284).

313344000 is an abundant number, since it is smaller than the sum of its proper divisors (882782568).

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

313344000 is an equidigital number, since it uses as much as digits as its factorization.

313344000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 66 (or 27 counting only the distinct ones).

The product of its (nonzero) digits is 432, while the sum is 18.

The square root of 313344000 is about 17701.5253580023. The cubic root of 313344000 is about 679.2147799020.

Adding to 313344000 its reverse (443313), we get a palindrome (313787313).

The spelling of 313344000 in words is "three hundred thirteen million, three hundred forty-four thousand".