462800 has 60 divisors (see below), whose sum is σ = 1210860. Its totient is φ = 168960.

The previous prime is 462773. The next prime is 462827. The reversal of 462800 is 8264.

It is an interprime number because it is at equal distance from previous prime (462773) and next prime (462827).

It can be written as a sum of positive squares in 6 ways, for example, as 107584 + 355216 = 328^2 + 596^2 .

It is a Harshad number since it is a multiple of its sum of digits (20).

It is a congruent number.

It is an unprimeable number.

462800 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 5156 + ... + 5244.

It is an arithmetic number, because the mean of its divisors is an integer number (20181).

2⁴⁶²⁸⁰⁰ is an apocalyptic number.

462800 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 462800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (605430).

462800 is an abundant number, since it is smaller than the sum of its proper divisors (748060).

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

462800 is a wasteful number, since it uses less digits than its factorization.

462800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 120 (or 109 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 20.

The square root of 462800 is about 680.2940540678. The cubic root of 462800 is about 77.3507359435.

The spelling of 462800 in words is "four hundred sixty-two thousand, eight hundred".