313213824 has 384 divisors, whose sum is σ = 1172102400. Its totient is φ = 80593920.

The previous prime is 313213819. The next prime is 313213829. The reversal of 313213824 is 428312313.

313213824 = T₄₀₁ + T₄₀₂ + ... + T₁₂₄₇.

It is an interprime number because it is at equal distance from previous prime (313213819) and next prime (313213829).

It is a tau number, because it is divible by the number of its divisors (384).

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

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (313213829) by changing a digit.

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, 2927179 + ... + 2927285.

It is an arithmetic number, because the mean of its divisors is an integer number (3052350).

Almost surely, 2^313213824 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 313213824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (586051200).

313213824 is an abundant number, since it is smaller than the sum of its proper divisors (858888576).

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

313213824 is a wasteful number, since it uses less digits than its factorization.

313213824 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 159 (or 130 counting only the distinct ones).

The product of its digits is 3456, while the sum is 27.

The square root of 313213824 is about 17697.8480047717. The cubic root of 313213824 is about 679.1207089448.

The spelling of 313213824 in words is "three hundred thirteen million, two hundred thirteen thousand, eight hundred twenty-four".