461580800 has 60 divisors (see below), whose sum is σ = 1143634206. Its totient is φ = 184627200.

The previous prime is 461580797. The next prime is 461580803. The reversal of 461580800 is 8085164.

It is an interprime number because it is at equal distance from previous prime (461580797) and next prime (461580803).

It can be written as a sum of positive squares in 3 ways, for example, as 288184576 + 173396224 = 16976^2 + 13168^2 .

It is a Harshad number since it is a multiple of its sum of digits (32).

It is not an unprimeable number, because it can be changed into a prime (461580803) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 5231 + ... + 30830.

Almost surely, 2^461580800 is an apocalyptic number.

461580800 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

461580800 is an abundant number, since it is smaller than the sum of its proper divisors (682053406).

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

461580800 is an equidigital number, since it uses as much as digits as its factorization.

461580800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 36089 (or 36068 counting only the distinct ones).

The product of its (nonzero) digits is 7680, while the sum is 32.

The square root of 461580800 is about 21484.4315726528. The cubic root of 461580800 is about 772.8275196775.

The spelling of 461580800 in words is "four hundred sixty-one million, five hundred eighty thousand, eight hundred".