462400 has 63 divisors (see below), whose sum is σ = 1208659. Its totient is φ = 174080.

The previous prime is 462377. The next prime is 462401. The reversal of 462400 is 4264.

The square root of 462400 is 680.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 4 ways, for example, as 10816 + 451584 = 104^2 + 672^2 .

It is a Harshad number since it is a multiple of its sum of digits (16).

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (462401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 27192 + ... + 27208.

462400 is a Friedman number, since it can be written as (640+40)^2, using all its digits and the basic arithmetic operations.

2⁴⁶²⁴⁰⁰ is an apocalyptic number.

462400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

462400 is the 680-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 462400

462400 is an abundant number, since it is smaller than the sum of its proper divisors (746259).

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

462400 is a wasteful number, since it uses less digits than its factorization.

462400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 56 (or 24 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 16.

The cubic root of 462400 is about 77.3284446639.

Multiplying 462400 by its sum of digits (16), we get a square (7398400 = 2720²).

462400 divided by its sum of digits (16) gives a square (28900 = 170²).

Adding to 462400 its reverse (4264), we get a palindrome (466664).

The spelling of 462400 in words is "four hundred sixty-two thousand, four hundred".