46656 has 49 divisors (see below), whose sum is σ = 138811. Its totient is φ = 15552.

The previous prime is 46649. The next prime is 46663. The reversal of 46656 is 65664.

46656 = T_{215} + T_{216}.

The square root of 46656 is 216.

The cubic root of 46656 is 36.

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

It is a Jordan-Polya number, since it can be written as (3!)^{6}.

46656 is a *`hidden beast`* number, since 4 + 6 + 656 = 666.

It is an interprime number because it is at equal distance from previous prime (46649) and next prime (46663).

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

It is a Duffinian number.

Its product of digits (4320) is a multiple of the sum of its prime divisors (5).

It is a nialpdrome in base 6, base 9 and base 16.

It is an unprimeable number.

It is a polite number, since it can be written in 6 ways as a sum of consecutive naturals, for example, 15551 + 15552 + 15553.

46656 is a Friedman number, since it can be written as 6^(6+5-4)/6, using all its digits and the basic arithmetic operations.

2^{46656} is an apocalyptic number.

46656 is the 216-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 46656

46656 is an abundant number, since it is smaller than the sum of its proper divisors (92155).

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

46656 is an frugal number, since it uses more digits than its factorization.

46656 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 30 (or 5 counting only the distinct ones).

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

Multiplying 46656 by its sum of digits (27), we get a cube (1259712 = 108^{3}).

46656 divided by its sum of digits (27) gives a cube (1728 = 12^{3}).

The spelling of 46656 in words is "forty-six thousand, six hundred fifty-six".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 144 162 192 216 243 288 324 432 486 576 648 729 864 972 1296 1458 1728 1944 2592 2916 3888 5184 5832 7776 11664 15552 23328 46656

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