461520 has 60 divisors (see below), whose sum is σ = 1552356. Its totient is φ = 122880.

The previous prime is 461507. The next prime is 461521. The reversal of 461520 is 25164.

It is a happy number.

It can be written as a sum of positive squares in 2 ways, for example, as 304704 + 156816 = 552^2 + 396^2 .

It is a tau number, because it is divible by the number of its divisors (60).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a junction number, because it is equal to n+sod(n) for n = 461493 and 461502.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 461520.

It is not an unprimeable number, because it can be changed into a prime (461521) by changing a digit.

461520 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 11 ways as a sum of consecutive naturals, for example, 400 + ... + 1040.

2⁴⁶¹⁵²⁰ is an apocalyptic number.

461520 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 461520, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (776178).

461520 is an abundant number, since it is smaller than the sum of its proper divisors (1090836).

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

461520 is a wasteful number, since it uses less digits than its factorization.

461520 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 660 (or 651 counting only the distinct ones).

The product of its (nonzero) digits is 240, while the sum is 18.

The square root of 461520 is about 679.3526330265. The cubic root of 461520 is about 77.2793585585.

Subtracting from 461520 its product of nonzero digits (240), we obtain a triangular number (461280 = T₉₆₀).

Adding to 461520 its reverse (25164), we get a palindrome (486684).

The spelling of 461520 in words is "four hundred sixty-one thousand, five hundred twenty".