312729984 has 320 divisors, whose sum is σ = 1105843200. Its totient is φ = 85847040.

The previous prime is 312729983. The next prime is 312730003. The reversal of 312729984 is 489927213.

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (312729983) 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 39 ways as a sum of consecutive naturals, for example, 2249787 + ... + 2249925.

It is an arithmetic number, because the mean of its divisors is an integer number (3455760).

Almost surely, 2^312729984 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 312729984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (552921600).

312729984 is an abundant number, since it is smaller than the sum of its proper divisors (793113216).

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

312729984 is a wasteful number, since it uses less digits than its factorization.

312729984 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 203 (or 182 counting only the distinct ones).

The product of its digits is 217728, while the sum is 45.

The square root of 312729984 is about 17684.1732631186. The cubic root of 312729984 is about 678.7708360259.

The spelling of 312729984 in words is "three hundred twelve million, seven hundred twenty-nine thousand, nine hundred eighty-four".