13009939735968 has 1728 divisors, whose sum is σ = 48044380849920. Its totient is φ = 3266077261824.

The previous prime is 13009939735937. The next prime is 13009939735993. The reversal of 13009939735968 is 86953793990031.

13009939735968 is a `hidden beast` number, since 1 + 30 + 0 + 99 + 397 + 35 + 96 + 8 = 666.

It is a super-2 number, since 2×13009939735968² (a number of 27 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (72).

It is a junction number, because it is equal to n+sod(n) for n = 13009939735896 and 13009939735905.

It is an unprimeable number.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 67409014080 + ... + 67409014272.

It is an arithmetic number, because the mean of its divisors is an integer number (27803461140).

Almost surely, 2^{13009939735968} is an apocalyptic number.

13009939735968 is a gapful number since it is divisible by the number (18) 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 13009939735968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (24022190424960).

13009939735968 is an abundant number, since it is smaller than the sum of its proper divisors (35034441113952).

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

13009939735968 is a wasteful number, since it uses less digits than its factorization.

13009939735968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 399 (or 371 counting only the distinct ones).

The product of its (nonzero) digits is 297606960, while the sum is 72.

The spelling of 13009939735968 in words is "thirteen trillion, nine billion, nine hundred thirty-nine million, seven hundred thirty-five thousand, nine hundred sixty-eight".