461761200 has 180 divisors, whose sum is σ = 1658070960. Its totient is φ = 118863360.

The previous prime is 461761189. The next prime is 461761211. The reversal of 461761200 is 2167164.

461761200 is a `hidden beast` number, since 46 + 1 + 7 + 612 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (461761189) and next prime (461761211).

It is a tau number, because it is divible by the number of its divisors (180).

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 102189 + ... + 106611.

Almost surely, 2^461761200 is an apocalyptic number.

461761200 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 461761200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (829035480).

461761200 is an abundant number, since it is smaller than the sum of its proper divisors (1196309760).

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

461761200 is a wasteful number, since it uses less digits than its factorization.

461761200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 4476 (or 4462 counting only the distinct ones).

The product of its (nonzero) digits is 2016, while the sum is 27.

The square root of 461761200 is about 21488.6295514628. The cubic root of 461761200 is about 772.9281881668.

The spelling of 461761200 in words is "four hundred sixty-one million, seven hundred sixty-one thousand, two hundred".