456168000 has 224 divisors, whose sum is σ = 1531071360. Its totient is φ = 119654400.

The previous prime is 456167963. The next prime is 456168001. The reversal of 456168000 is 861654.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (456168001) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 1991886 + ... + 1992114.

It is an arithmetic number, because the mean of its divisors is an integer number (6835140).

Almost surely, 2^456168000 is an apocalyptic number.

456168000 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 456168000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (765535680).

456168000 is an abundant number, since it is smaller than the sum of its proper divisors (1074903360).

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

456168000 is a wasteful number, since it uses less digits than its factorization.

456168000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 342 (or 322 counting only the distinct ones).

The product of its (nonzero) digits is 5760, while the sum is 30.

The square root of 456168000 is about 21358.0898022272. The cubic root of 456168000 is about 769.7947392386.

The spelling of 456168000 in words is "four hundred fifty-six million, one hundred sixty-eight thousand".