999 has 8 divisors (see below), whose sum is σ = 1520. Its totient is φ = 648.

The previous prime is 997. The next prime is 1009.

Adding to 999 its product of digits (729), we get a cube (1728 = 12^{3}).

999 is nontrivially palindromic in base 10 and base 14.

It is a Cunningham number, because it is equal to 10^{3}-1.

999 is an esthetic number in base 6, because in such base its adjacent digits differ by 1.

It is a trimorphic number since its cube, 997002999, ends in 999.

It is not a de Polignac number, because 999 - 2^{1} = 997 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (27), and also a Moran number because the ratio is a prime number: 37 = 999 / (9 + 9 + 9).

It is a nude number because it is divisible by every one of its digits.

It is a Duffinian number.

999 is an undulating number in base 6 and base 14.

999 is a modest number, since divided by 99 gives 9 as remainder.

999 is a nontrivial repdigit in base 10.

It is a plaindrome in base 5, base 10, base 13 and base 15.

It is a nialpdrome in base 10.

It is a zygodrome in base 2 and base 10.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (991) by changing a digit.

It is a Kaprekar number, because its square (998001) can be partitioned into two parts whose sum is 999.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 9 + ... + 45.

It is an arithmetic number, because the mean of its divisors is an integer number (190).

999 is a deficient number, since it is larger than the sum of its proper divisors (521).

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

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

The sum of its prime factors is 46 (or 40 counting only the distinct ones).

The product of its digits is 729, while the sum is 27.

The square root of 999 is about 31.6069612586. The cubic root of 999 is about 9.9966655549.

The spelling of 999 in words is "nine hundred ninety-nine", and thus it is an aban number and an oban number.

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