313372800 has 576 divisors, whose sum is σ = 1289084160. Its totient is φ = 74649600.

The previous prime is 313372751. The next prime is 313372823. The reversal of 313372800 is 8273313.

It is a tau number, because it is divible by the number of its divisors (576).

It is a super-3 number, since 3×313372800³ (a number of 26 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 10108785 + ... + 10108815.

Almost surely, 2^313372800 is an apocalyptic number.

313372800 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 313372800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (644542080).

313372800 is an abundant number, since it is smaller than the sum of its proper divisors (975711360).

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

313372800 is a wasteful number, since it uses less digits than its factorization.

313372800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 83 (or 54 counting only the distinct ones).

The product of its (nonzero) digits is 3024, while the sum is 27.

The square root of 313372800 is about 17702.3388285277. The cubic root of 313372800 is about 679.2355885409.

The spelling of 313372800 in words is "three hundred thirteen million, three hundred seventy-two thousand, eight hundred".