459972 has 24 divisors (see below), whose sum is σ = 1192800. Its totient is φ = 153288.

The previous prime is 459961. The next prime is 460013. The reversal of 459972 is 279954.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 2022 + ... + 2237.

It is an arithmetic number, because the mean of its divisors is an integer number (49700).

2⁴⁵⁹⁹⁷² is an apocalyptic number.

It is an amenable number.

459972 is an abundant number, since it is smaller than the sum of its proper divisors (732828).

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

459972 is a wasteful number, since it uses less digits than its factorization.

459972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 4272 (or 4264 counting only the distinct ones).

The product of its digits is 22680, while the sum is 36.

The square root of 459972 is about 678.2123561245. The cubic root of 459972 is about 77.1928599981.

It can be divided in two parts, 459 and 972, that added together give a triangular number (1431 = T₅₃).

The spelling of 459972 in words is "four hundred fifty-nine thousand, nine hundred seventy-two".