6838416000 has 576 divisors, whose sum is σ = 26687526840. Its totient is φ = 1677312000.

The previous prime is 6838415999. The next prime is 6838416007. The reversal of 6838416000 is 6148386.

It is a happy number.

6838416000 is a `hidden beast` number, since 6 + 8 + 3 + 8 + 41 + 600 + 0 = 666.

It can be written as a sum of positive squares in 12 ways, for example, as 1650959424 + 5187456576 = 40632^2 + 72024^2 .

It is a tau number, because it is divible by the number of its divisors (576).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (6838416007) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 24335860 + ... + 24336140.

Almost surely, 2^6838416000 is an apocalyptic number.

6838416000 is a gapful number since it is divisible by the number (60) 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 6838416000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (13343763420).

6838416000 is an abundant number, since it is smaller than the sum of its proper divisors (19849110840).

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

6838416000 is a wasteful number, since it uses less digits than its factorization.

6838416000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 342 (or 304 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 36.

The square root of 6838416000 is about 82694.7156715591. The cubic root of 6838416000 is about 1898.0974491781.

The spelling of 6838416000 in words is "six billion, eight hundred thirty-eight million, four hundred sixteen thousand".