46656000 has 280 divisors, whose sum is σ = 174429684. Its totient is φ = 12441600.

The previous prime is 46655981. The next prime is 46656011. The reversal of 46656000 is 65664.

The cubic root of 46656000 is 360.

It is a perfect power (a cube), and thus also a powerful number.

46656000 is a `hidden beast` number, since 4 + 6 + 656 + 0 + 0 + 0 = 666.

It can be written as a sum of positive squares in 2 ways, for example, as 31539456 + 15116544 = 5616^2 + 3888^2 .

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

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 27 ways as a sum of consecutive naturals, for example, 9331198 + ... + 9331202.

Almost surely, 2^46656000 is an apocalyptic number.

46656000 is a gapful number since it is divisible by the number (40) 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 46656000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (87214842).

46656000 is an abundant number, since it is smaller than the sum of its proper divisors (127773684).

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

46656000 is an frugal number, since it uses more digits than its factorization.

46656000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 51 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 4320, while the sum is 27.

The square root of 46656000 is about 6830.5197459637.

Multiplying 46656000 by its sum of digits (27), we get a cube (1259712000 = 1080³).

46656000 divided by its sum of digits (27) gives a cube (1728000 = 120³).

The spelling of 46656000 in words is "forty-six million, six hundred fifty-six thousand".