13638977510400 has 1980 divisors, whose sum is σ = 58454260797240. Its totient is φ = 3131301888000.

The previous prime is 13638977510369. The next prime is 13638977510429. The reversal of 13638977510400 is 401577983631.

13638977510400 is a `hidden beast` number, since 1 + 3 + 6 + 3 + 89 + 7 + 7 + 510 + 40 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1980).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 179 ways as a sum of consecutive naturals, for example, 4767204970 + ... + 4767207830.

It is an arithmetic number, because the mean of its divisors is an integer number (29522353938).

Almost surely, 2^{13638977510400} is an apocalyptic number.

13638977510400 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 13638977510400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (29227130398620).

13638977510400 is an abundant number, since it is smaller than the sum of its proper divisors (44815283286840).

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

13638977510400 is a wasteful number, since it uses less digits than its factorization.

13638977510400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2944 (or 2901 counting only the distinct ones).

The product of its (nonzero) digits is 3810240, while the sum is 54.

The spelling of 13638977510400 in words is "thirteen trillion, six hundred thirty-eight billion, nine hundred seventy-seven million, five hundred ten thousand, four hundred".