313420800 has 528 divisors, whose sum is σ = 1315844352. Its totient is φ = 63897600.

The previous prime is 313420771. The next prime is 313420817. The reversal of 313420800 is 8024313.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (528).

It is a Harshad number since it is a multiple of its sum of digits (21).

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 47 ways as a sum of consecutive naturals, for example, 5913574 + ... + 5913626.

Almost surely, 2^313420800 is an apocalyptic number.

313420800 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 313420800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (657922176).

313420800 is an abundant number, since it is smaller than the sum of its proper divisors (1002423552).

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

313420800 is a wasteful number, since it uses less digits than its factorization.

313420800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 104 (or 81 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 21.

The square root of 313420800 is about 17703.6945296737. The cubic root of 313420800 is about 679.2702667726.

The spelling of 313420800 in words is "three hundred thirteen million, four hundred twenty thousand, eight hundred".