461926800 has 300 divisors, whose sum is σ = 1695376980. Its totient is φ = 120407040.

The previous prime is 461926799. The next prime is 461926807. The reversal of 461926800 is 8629164.

It can be written as a sum of positive squares in 6 ways, for example, as 37896336 + 424030464 = 6156^2 + 20592^2 .

It is a tau number, because it is divible by the number of its divisors (300).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (461926807) by changing a digit.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 1717066 + ... + 1717334.

Almost surely, 2^461926800 is an apocalyptic number.

461926800 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 461926800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (847688490).

461926800 is an abundant number, since it is smaller than the sum of its proper divisors (1233450180).

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

461926800 is a wasteful number, since it uses less digits than its factorization.

461926800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 352 (or 332 counting only the distinct ones).

The product of its (nonzero) digits is 20736, while the sum is 36.

The square root of 461926800 is about 21492.4824066463. The cubic root of 461926800 is about 773.0205747438.

Subtracting from 461926800 its product of nonzero digits (20736), we obtain a square (461906064 = 21492²).

The spelling of 461926800 in words is "four hundred sixty-one million, nine hundred twenty-six thousand, eight hundred".