315648000 has 288 divisors, whose sum is σ = 1146043080. Its totient is φ = 83558400.

The previous prime is 315647989. The next prime is 315648013. The reversal of 315648000 is 846513.

315648000 is a `hidden beast` number, since 3 + 15 + 648 + 0 + 0 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 105513984 + 210134016 = 10272^2 + 14496^2 .

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

It is a super-3 number, since 3×315648000³ (a number of 26 digits) contains 333 as substring.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 2303932 + ... + 2304068.

Almost surely, 2^315648000 is an apocalyptic number.

315648000 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 315648000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (573021540).

315648000 is an abundant number, since it is smaller than the sum of its proper divisors (830395080).

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

315648000 is a wasteful number, since it uses less digits than its factorization.

315648000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 180 (or 147 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 27.

The square root of 315648000 is about 17766.4853023889. The cubic root of 315648000 is about 680.8754583458.

The spelling of 315648000 in words is "three hundred fifteen million, six hundred forty-eight thousand".