13038107846400 has 4536 divisors, whose sum is σ = 62672741594064. Its totient is φ = 2658720153600.

The previous prime is 13038107846363. The next prime is 13038107846411. The reversal of 13038107846400 is 464870183031.

13038107846400 is a `hidden beast` number, since 1 + 30 + 38 + 107 + 84 + 6 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (4536).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 503 ways as a sum of consecutive naturals, for example, 121851475147 + ... + 121851475253.

It is an arithmetic number, because the mean of its divisors is an integer number (13816741974).

Almost surely, 2^{13038107846400} is an apocalyptic number.

13038107846400 is a gapful number since it is divisible by the number (10) 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 13038107846400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (31336370797032).

13038107846400 is an abundant number, since it is smaller than the sum of its proper divisors (49634633747664).

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

13038107846400 is a wasteful number, since it uses less digits than its factorization.

13038107846400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 219 (or 178 counting only the distinct ones).

The product of its (nonzero) digits is 387072, while the sum is 45.

The spelling of 13038107846400 in words is "thirteen trillion, thirty-eight billion, one hundred seven million, eight hundred forty-six thousand, four hundred".