4731616800 has 864 divisors, whose sum is σ = 19303764480. Its totient is φ = 1083801600.

The previous prime is 4731616789. The next prime is 4731616801. The reversal of 4731616800 is 86161374.

4731616800 is a `hidden beast` number, since 4 + 7 + 31 + 616 + 8 + 0 + 0 = 666.

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 (4731616801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 110037579 + ... + 110037621.

It is an arithmetic number, because the mean of its divisors is an integer number (22342320).

Almost surely, 2^4731616800 is an apocalyptic number.

4731616800 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 4731616800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (9651882240).

4731616800 is an abundant number, since it is smaller than the sum of its proper divisors (14572147680).

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

4731616800 is a wasteful number, since it uses less digits than its factorization.

4731616800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 146 (or 130 counting only the distinct ones).

The product of its (nonzero) digits is 24192, while the sum is 36.

The square root of 4731616800 is about 68786.7487238640. The cubic root of 4731616800 is about 1678.8163431121.

The spelling of 4731616800 in words is "four billion, seven hundred thirty-one million, six hundred sixteen thousand, eight hundred".