313408800 has 432 divisors, whose sum is σ = 1218672000. Its totient is φ = 75479040.

The previous prime is 313408763. The next prime is 313408807. The reversal of 313408800 is 8804313.

It is not an unprimeable number, because it can be changed into a prime (313408807) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 3967161 + ... + 3967239.

It is an arithmetic number, because the mean of its divisors is an integer number (2821000).

Almost surely, 2^313408800 is an apocalyptic number.

313408800 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 313408800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (609336000).

313408800 is an abundant number, since it is smaller than the sum of its proper divisors (905263200).

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

313408800 is a wasteful number, since it uses less digits than its factorization.

313408800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 153 (or 137 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The square root of 313408800 is about 17703.3556141202. The cubic root of 313408800 is about 679.2615975466.

The spelling of 313408800 in words is "three hundred thirteen million, four hundred eight thousand, eight hundred".