459680 has 72 divisors (see below), whose sum is σ = 1245132. Its totient is φ = 159744.

The previous prime is 459677. The next prime is 459691. The reversal of 459680 is 86954.

459680 = T₂₂₄ + T₂₂₅ + ... + T₂₄₀.

459680 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 6 ways, for example, as 94864 + 364816 = 308^2 + 604^2 .

It is a super-2 number, since 2×459680² = 422611404800, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (32).

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 11 ways as a sum of consecutive naturals, for example, 27032 + ... + 27048.

2⁴⁵⁹⁶⁸⁰ is an apocalyptic number.

459680 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 459680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (622566).

459680 is an abundant number, since it is smaller than the sum of its proper divisors (785452).

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

459680 is a wasteful number, since it uses less digits than its factorization.

459680 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 58 (or 37 counting only the distinct ones).

The product of its (nonzero) digits is 8640, while the sum is 32.

The square root of 459680 is about 677.9970501411. The cubic root of 459680 is about 77.1765219844.

459680 divided by its sum of digits (32) gives a triangular number (14365 = T₁₆₉).

It can be divided in two parts, 45 and 9680, that multiplied together give a square (435600 = 660²).

The spelling of 459680 in words is "four hundred fifty-nine thousand, six hundred eighty".