456 has 16 divisors (see below), whose sum is σ = 1200. Its totient is φ = 144.

The previous prime is 449. The next prime is 457. The reversal of 456 is 654.

Subtracting from 456 its sum of digits (15), we obtain a square (441 = 21^{2}).

Adding to 456 its product of digits (120), we get a square (576 = 24^{2}).

456 is nontrivially palindromic in base 7.

456 is an esthetic number in base 10, because in such base its adjacent digits differ by 1.

It is a hoax number, since the sum of its digits (15) coincides with the sum of the digits of its distinct prime factors.

It is an Ulam number.

It is an alternating number because its digits alternate between even and odd.

Its product of digits (120) is a multiple of the sum of its prime divisors (24).

It is a straight-line number, since its digits are in arithmetic progression.

It is a plaindrome in base 9, base 10 and base 14.

It is a nialpdrome in base 5, base 8 and base 12.

It is a zygodrome in base 5.

It is not an unprimeable number, because it can be changed into a prime (457) by changing a digit.

It is an upside-down number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 15 + ... + 33.

It is an arithmetic number, because the mean of its divisors is an integer number (75).

456 is the 14-th centered pentagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 456, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (600).

456 is an abundant number, since it is smaller than the sum of its proper divisors (744).

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

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

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

The sum of its prime factors is 28 (or 24 counting only the distinct ones).

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

The square root of 456 is about 21.3541565041. The cubic root of 456 is about 7.6970022626.

The spelling of 456 in words is "four hundred fifty-six", and thus it is an aban number.

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