315972000 has 288 divisors, whose sum is σ = 1146809664. Its totient is φ = 82368000.

The previous prime is 315971989. The next prime is 315972017. The reversal of 315972000 is 279513.

It is a tau number, because it is divible by the number of its divisors (288).

It is an unprimeable number.

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 47 ways as a sum of consecutive naturals, for example, 2411935 + ... + 2412065.

It is an arithmetic number, because the mean of its divisors is an integer number (3981978).

Almost surely, 2^315972000 is an apocalyptic number.

315972000 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 315972000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (573404832).

315972000 is an abundant number, since it is smaller than the sum of its proper divisors (830837664).

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

315972000 is a wasteful number, since it uses less digits than its factorization.

315972000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 229 (or 208 counting only the distinct ones).

The product of its (nonzero) digits is 1890, while the sum is 27.

The square root of 315972000 is about 17775.6012556538. The cubic root of 315972000 is about 681.1083424564.

It can be divided in two parts, 315 and 972000, that added together give a triangular number (972315 = T₁₃₉₄).

The spelling of 315972000 in words is "three hundred fifteen million, nine hundred seventy-two thousand".