457984800 has 576 divisors, whose sum is σ = 2047368960. Its totient is φ = 96215040.

The previous prime is 457984789. The next prime is 457984817. The reversal of 457984800 is 8489754.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 1965484 + ... + 1965716.

It is an arithmetic number, because the mean of its divisors is an integer number (3554460).

Almost surely, 2^457984800 is an apocalyptic number.

457984800 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 457984800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1023684480).

457984800 is an abundant number, since it is smaller than the sum of its proper divisors (1589384160).

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

457984800 is a wasteful number, since it uses less digits than its factorization.

457984800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 282 (or 263 counting only the distinct ones).

The product of its (nonzero) digits is 322560, while the sum is 45.

The square root of 457984800 is about 21400.5794314079. The cubic root of 457984800 is about 770.8153504124.

The spelling of 457984800 in words is "four hundred fifty-seven million, nine hundred eighty-four thousand, eight hundred".