3006676310400 has 1152 divisors, whose sum is σ = 13323342489600. Its totient is φ = 630042624000.

The previous prime is 3006676310389. The next prime is 3006676310401. The reversal of 3006676310400 is 40136766003.

It is a happy number.

3006676310400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (1152).

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 (3006676310401) by changing a digit.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 118729740 + ... + 118755060.

Almost surely, 2^{3006676310400} is an apocalyptic number.

3006676310400 is a gapful number since it is divisible by the number (30) 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 3006676310400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (6661671244800).

3006676310400 is an abundant number, since it is smaller than the sum of its proper divisors (10316666179200).

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

3006676310400 is a wasteful number, since it uses less digits than its factorization.

3006676310400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 25408 (or 25388 counting only the distinct ones).

The product of its (nonzero) digits is 54432, while the sum is 36.

The spelling of 3006676310400 in words is "three trillion, six billion, six hundred seventy-six million, three hundred ten thousand, four hundred".