461888640 has 384 divisors, whose sum is σ = 1739977200. Its totient is φ = 112459776.

The previous prime is 461888633. The next prime is 461888641. The reversal of 461888640 is 46888164.

It can be written as a sum of positive squares in 8 ways, for example, as 242611776 + 219276864 = 15576^2 + 14808^2 .

It is a tau number, because it is divible by the number of its divisors (384).

It is a super-2 number, since 2×461888640² = 426682231522099200, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (461888641) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 5189716 + ... + 5189804.

Almost surely, 2^461888640 is an apocalyptic number.

461888640 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 461888640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (869988600).

461888640 is an abundant number, since it is smaller than the sum of its proper divisors (1278088560).

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

461888640 is a wasteful number, since it uses less digits than its factorization.

461888640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 184 (or 169 counting only the distinct ones).

The product of its (nonzero) digits is 294912, while the sum is 45.

The square root of 461888640 is about 21491.5946360432. The cubic root of 461888640 is about 772.9992876211. Note that the first 3 decimals are identical.

The spelling of 461888640 in words is "four hundred sixty-one million, eight hundred eighty-eight thousand, six hundred forty".