612864000 has 624 divisors, whose sum is σ = 2657815680. Its totient is φ = 132710400.

The previous prime is 612863983. The next prime is 612864001. The reversal of 612864000 is 468216.

612864000 is a `hidden beast` number, since 6 + 12 + 8 + 640 + 0 + 0 = 666.

It is a hoax number, since the sum of its digits (27) coincides with the sum of the digits of its distinct prime factors.

It is not an unprimeable number, because it can be changed into a prime (612864001) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 32255991 + ... + 32256009.

It is an arithmetic number, because the mean of its divisors is an integer number (4259320).

Almost surely, 2^612864000 is an apocalyptic number.

612864000 is a gapful number since it is divisible by the number (60) 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 612864000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1328907840).

612864000 is an abundant number, since it is smaller than the sum of its proper divisors (2044951680).

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

612864000 is a wasteful number, since it uses less digits than its factorization.

612864000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 71 (or 36 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The square root of 612864000 is about 24756.0901597970. The cubic root of 612864000 is about 849.4178251128.

The spelling of 612864000 in words is "six hundred twelve million, eight hundred sixty-four thousand".