456840 has 96 divisors (see below), whose sum is σ = 1572480. Its totient is φ = 119232.

The previous prime is 456821. The next prime is 456871. The reversal of 456840 is 48654.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

456840 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 23 ways as a sum of consecutive naturals, for example, 9697 + ... + 9743.

It is an arithmetic number, because the mean of its divisors is an integer number (16380).

456840 is a Friedman number, since it can be written as 846*540, using all its digits and the basic arithmetic operations.

It is a vampire number, since it can be written as 540 ⋅ 846 (with its own digits).

2⁴⁵⁶⁸⁴⁰ is an apocalyptic number.

456840 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 456840, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (786240).

456840 is an abundant number, since it is smaller than the sum of its proper divisors (1115640).

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

456840 is a wasteful number, since it uses less digits than its factorization.

456840 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 73 (or 57 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 27.

The square root of 456840 is about 675.8994007987. The cubic root of 456840 is about 77.0172559291.

It can be divided in two parts, 456 and 840, that added together give a 4-th power (1296 = 6⁴).

The spelling of 456840 in words is "four hundred fifty-six thousand, eight hundred forty".