4616438400 has 768 divisors, whose sum is σ = 20489760000. Its totient is φ = 990904320.

The previous prime is 4616438363. The next prime is 4616438413. The reversal of 4616438400 is 48346164.

4616438400 is a `hidden beast` number, since 4 + 6 + 1 + 643 + 8 + 4 + 0 + 0 = 666.

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

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 10281376 + ... + 10281824.

It is an arithmetic number, because the mean of its divisors is an integer number (26679375).

Almost surely, 2^4616438400 is an apocalyptic number.

4616438400 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 4616438400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (10244880000).

4616438400 is an abundant number, since it is smaller than the sum of its proper divisors (15873321600).

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

4616438400 is a wasteful number, since it uses less digits than its factorization.

4616438400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 506 (or 483 counting only the distinct ones).

The product of its (nonzero) digits is 55296, while the sum is 36.

The square root of 4616438400 is about 67944.3772508071. The cubic root of 4616438400 is about 1665.0822132929.

The spelling of 4616438400 in words is "four billion, six hundred sixteen million, four hundred thirty-eight thousand, four hundred".