312961920 has 256 divisors, whose sum is σ = 1098662400. Its totient is φ = 75423744.

The previous prime is 312961919. The next prime is 312961921. The reversal of 312961920 is 29169213.

It is an interprime number because it is at equal distance from previous prime (312961919) and next prime (312961921).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (312961921) 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 31 ways as a sum of consecutive naturals, for example, 838854 + ... + 839226.

It is an arithmetic number, because the mean of its divisors is an integer number (4291650).

Almost surely, 2^312961920 is an apocalyptic number.

312961920 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 312961920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (549331200).

312961920 is an abundant number, since it is smaller than the sum of its proper divisors (785700480).

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

312961920 is a wasteful number, since it uses less digits than its factorization.

312961920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 437 (or 425 counting only the distinct ones).

The product of its (nonzero) digits is 5832, while the sum is 33.

The square root of 312961920 is about 17690.7297757894. The cubic root of 312961920 is about 678.9385978834.

The spelling of 312961920 in words is "three hundred twelve million, nine hundred sixty-one thousand, nine hundred twenty".