456768 has 84 divisors (see below), whose sum is σ = 1433068. Its totient is φ = 138240.

The previous prime is 456767. The next prime is 456769. The reversal of 456768 is 867654.

It is a happy number.

456768 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (456767) and next prime (456769).

It can be written as a sum of positive squares in 2 ways, for example, as 36864 + 419904 = 192^2 + 648^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a nialpdrome in base 9.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (456763) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 7458 + ... + 7518.

2⁴⁵⁶⁷⁶⁸ is an apocalyptic number.

456768 is a gapful number since it is divisible by the number (48) 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 456768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (716534).

456768 is an abundant number, since it is smaller than the sum of its proper divisors (976300).

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

456768 is a wasteful number, since it uses less digits than its factorization.

456768 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 92 (or 79 counting only the distinct ones).

The product of its digits is 40320, while the sum is 36.

The square root of 456768 is about 675.8461363358. The cubic root of 456768 is about 77.0132096300.

The spelling of 456768 in words is "four hundred fifty-six thousand, seven hundred sixty-eight".