46656000000 has 637 divisors, whose sum is σ = 174856414153. Its totient is φ = 12441600000.

The previous prime is 46655999989. The next prime is 46656000007. The reversal of 46656000000 is 65664.

The square root of 46656000000 is 216000.

The cubic root of 46656000000 is 3600.

It is a perfect power (a square, a cube, a 6-th power), and thus also a powerful number.

46656000000 is a `hidden beast` number, since 4 + 6 + 656 + 0 + 0 + 0 + 0 + 0 + 0 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 40875134976 + 5780865024 = 202176^2 + 76032^2 .

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

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (46656000007) by changing a digit.

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 48 ways as a sum of consecutive naturals, for example, 9331199998 + ... + 9331200002.

Almost surely, 2^46656000000 is an apocalyptic number.

46656000000 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

46656000000 is the 216000-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 46656000000

46656000000 is an abundant number, since it is smaller than the sum of its proper divisors (128200414153).

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

46656000000 is an frugal number, since it uses more digits than its factorization.

46656000000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 72 (or 10 counting only the distinct ones).

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

Multiplying 46656000000 by its sum of digits (27), we get a cube (1259712000000 = 10800³).

46656000000 divided by its sum of digits (27) gives a cube (1728000000 = 1200³).

Adding to 46656000000 its reverse (65664), we get a palindrome (46656065664).

The spelling of 46656000000 in words is "forty-six billion, six hundred fifty-six million", and thus it is an aban number.