457600 has 96 divisors (see below), whose sum is σ = 1328040. Its totient is φ = 153600.

The previous prime is 457571. The next prime is 457607. The reversal of 457600 is 6754.

457600 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (22).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (457607) 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, 35194 + ... + 35206.

457600 is a Friedman number, since it can be written as 7040*65, using all its digits and the basic arithmetic operations.

It is a vampire number, since it can be written as 650 ⋅ 704 (with its own digits).

2⁴⁵⁷⁶⁰⁰ is an apocalyptic number.

457600 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 457600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (664020).

457600 is an abundant number, since it is smaller than the sum of its proper divisors (870440).

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

457600 is a wasteful number, since it uses less digits than its factorization.

457600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 48 (or 31 counting only the distinct ones).

The product of its (nonzero) digits is 840, while the sum is 22.

The square root of 457600 is about 676.4613810115. The cubic root of 457600 is about 77.0599409580.

It can be divided in two parts, 4 and 57600, that multiplied together give a square (230400 = 480²).

The spelling of 457600 in words is "four hundred fifty-seven thousand, six hundred".