13385648102400 has 792 divisors, whose sum is σ = 54891178168320. Its totient is φ = 3053013073920.

The previous prime is 13385648102371. The next prime is 13385648102423. The reversal of 13385648102400 is 420184658331.

13385648102400 is a `hidden beast` number, since 1 + 3 + 3 + 8 + 564 + 81 + 0 + 2 + 4 + 0 + 0 = 666.

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 polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 772522537 + ... + 772539863.

Almost surely, 2^{13385648102400} is an apocalyptic number.

13385648102400 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 13385648102400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (27445589084160).

13385648102400 is an abundant number, since it is smaller than the sum of its proper divisors (41505530065920).

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

13385648102400 is a wasteful number, since it uses less digits than its factorization.

13385648102400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 17849 (or 17823 counting only the distinct ones).

The product of its (nonzero) digits is 552960, while the sum is 45.

The spelling of 13385648102400 in words is "thirteen trillion, three hundred eighty-five billion, six hundred forty-eight million, one hundred two thousand, four hundred".