456000 has 112 divisors (see below), whose sum is σ = 1584960. Its totient is φ = 115200.

The previous prime is 455999. The next prime is 456007. The reversal of 456000 is 654.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (456007) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 23991 + ... + 24009.

2⁴⁵⁶⁰⁰⁰ is an apocalyptic number.

456000 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 456000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (792480).

456000 is an abundant number, since it is smaller than the sum of its proper divisors (1128960).

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

456000 is a wasteful number, since it uses less digits than its factorization.

456000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 49 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 120, while the sum is 15.

The square root of 456000 is about 675.2777206454. The cubic root of 456000 is about 76.9700226255.

Adding to 456000 its reverse (654), we get a palindrome (456654).

The spelling of 456000 in words is "four hundred fifty-six thousand".