457977920400 has 1920 divisors, whose sum is σ = 2219871252480. Its totient is φ = 87675955200.

The previous prime is 457977920371. The next prime is 457977920401. The reversal of 457977920400 is 4029779754.

457977920400 is a `hidden beast` number, since 4 + 579 + 7 + 7 + 9 + 20 + 40 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is not an unprimeable number, because it can be changed into a prime (457977920401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 383 ways as a sum of consecutive naturals, for example, 875674539 + ... + 875675061.

It is an arithmetic number, because the mean of its divisors is an integer number (1156182944).

Almost surely, 2^457977920400 is an apocalyptic number.

457977920400 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 457977920400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1109935626240).

457977920400 is an abundant number, since it is smaller than the sum of its proper divisors (1761893332080).

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

457977920400 is a wasteful number, since it uses less digits than its factorization.

457977920400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 593 (or 564 counting only the distinct ones).

The product of its (nonzero) digits is 4445280, while the sum is 54.

The spelling of 457977920400 in words is "four hundred fifty-seven billion, nine hundred seventy-seven million, nine hundred twenty thousand, four hundred".