456253200 has 180 divisors, whose sum is σ = 1705294500. Its totient is φ = 112296960.

The previous prime is 456253163. The next prime is 456253211. The reversal of 456253200 is 2352654.

456253200 is a `hidden beast` number, since 4 + 5 + 625 + 32 + 0 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 118722816 + 337530384 = 10896^2 + 18372^2 .

It is a tau number, because it is divible by the number of its divisors (180).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 41926 + ... + 51674.

Almost surely, 2^456253200 is an apocalyptic number.

456253200 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 456253200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (852647250).

456253200 is an abundant number, since it is smaller than the sum of its proper divisors (1249041300).

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

456253200 is a wasteful number, since it uses less digits than its factorization.

456253200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 9786 (or 9772 counting only the distinct ones).

The product of its (nonzero) digits is 7200, while the sum is 27.

The square root of 456253200 is about 21360.0842694967. The cubic root of 456253200 is about 769.8426619549.

The spelling of 456253200 in words is "four hundred fifty-six million, two hundred fifty-three thousand, two hundred".