321264000 has 384 divisors, whose sum is σ = 1216313280. Its totient is φ = 81100800.

The previous prime is 321263963. The next prime is 321264017. The reversal of 321264000 is 462123.

It is a happy number.

321264000 is a `hidden beast` number, since 3 + 21 + 2 + 640 + 0 + 0 = 666.

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 (18).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 3311952 + ... + 3312048.

Almost surely, 2^321264000 is an apocalyptic number.

321264000 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 321264000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (608156640).

321264000 is an abundant number, since it is smaller than the sum of its proper divisors (895049280).

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

321264000 is a wasteful number, since it uses less digits than its factorization.

321264000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 155 (or 130 counting only the distinct ones).

The product of its (nonzero) digits is 288, while the sum is 18.

The square root of 321264000 is about 17923.8388745269. The cubic root of 321264000 is about 684.8897828246.

The spelling of 321264000 in words is "three hundred twenty-one million, two hundred sixty-four thousand".