461312 has 40 divisors (see below), whose sum is σ = 994356. Its totient is φ = 212992.

The previous prime is 461309. The next prime is 461317. The reversal of 461312 is 213164.

It can be written as a sum of positive squares in 2 ways, for example, as 430336 + 30976 = 656^2 + 176^2 .

It is a super-2 number, since 2×461312² = 425617522688, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (17).

Its product of digits (144) is a multiple of the sum of its prime divisors (72).

It is not an unprimeable number, because it can be changed into a prime (461317) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 8678 + ... + 8730.

2⁴⁶¹³¹² 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 461312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (497178).

461312 is an abundant number, since it is smaller than the sum of its proper divisors (533044).

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

461312 is an equidigital number, since it uses as much as digits as its factorization.

461312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 88 (or 72 counting only the distinct ones).

The product of its digits is 144, while the sum is 17.

The square root of 461312 is about 679.1995288573. The cubic root of 461312 is about 77.2677472726.

Adding to 461312 its reverse (213164), we get a palindrome (674476).

It can be divided in two parts, 4 and 61312, that added together give a palindrome (61316).

The spelling of 461312 in words is "four hundred sixty-one thousand, three hundred twelve".