456800 has 36 divisors (see below), whose sum is σ = 1117116. Its totient is φ = 182400.

The previous prime is 456791. The next prime is 456809. The reversal of 456800 is 8654.

It is an interprime number because it is at equal distance from previous prime (456791) and next prime (456809).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (456809) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 515 + ... + 1085.

It is an arithmetic number, because the mean of its divisors is an integer number (31031).

2⁴⁵⁶⁸⁰⁰ is an apocalyptic number.

456800 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 456800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (558558).

456800 is an abundant number, since it is smaller than the sum of its proper divisors (660316).

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

456800 is a wasteful number, since it uses less digits than its factorization.

456800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 591 (or 578 counting only the distinct ones).

The product of its (nonzero) digits is 960, while the sum is 23.

The square root of 456800 is about 675.8698099486. The cubic root of 456800 is about 77.0150080377.

The spelling of 456800 in words is "four hundred fifty-six thousand, eight hundred".