461952 has 48 divisors (see below), whose sum is σ = 1332630. Its totient is φ = 153600.

The previous prime is 461933. The next prime is 461957. The reversal of 461952 is 259164.

It can be written as a sum of positive squares in only one way, i.e., 254016 + 207936 = 504^2 + 456^2 .

It is a tau number, because it is divible by the number of its divisors (48).

It is not an unprimeable number, because it can be changed into a prime (461957) by changing a digit.

461952 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 952 + ... + 1352.

2⁴⁶¹⁹⁵² 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 461952, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (666315).

461952 is an abundant number, since it is smaller than the sum of its proper divisors (870678).

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

461952 is a wasteful number, since it uses less digits than its factorization.

461952 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 421 (or 406 counting only the distinct ones).

The product of its digits is 2160, while the sum is 27.

The square root of 461952 is about 679.6705084083. The cubic root of 461952 is about 77.3034631635.

The spelling of 461952 in words is "four hundred sixty-one thousand, nine hundred fifty-two".