465972 has 48 divisors (see below), whose sum is σ = 1223040. Its totient is φ = 137088.

The previous prime is 465947. The next prime is 465977. The reversal of 465972 is 279564.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (465977) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 4473 + ... + 4575.

It is an arithmetic number, because the mean of its divisors is an integer number (25480).

2⁴⁶⁵⁹⁷² is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 465972, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (611520).

465972 is an abundant number, since it is smaller than the sum of its proper divisors (757068).

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

465972 is a wasteful number, since it uses less digits than its factorization.

465972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 152 (or 150 counting only the distinct ones).

The product of its digits is 15120, while the sum is 33.

The square root of 465972 is about 682.6214177712. The cubic root of 465972 is about 77.5270526438.

The spelling of 465972 in words is "four hundred sixty-five thousand, nine hundred seventy-two".