29972413669968 has 1920 divisors, whose sum is σ = 114494271897600. Its totient is φ = 7418080051200.

The previous prime is 29972413669967. The next prime is 29972413669993. The reversal of 29972413669968 is 86996631427992.

29972413669968 is a `hidden beast` number, since 2 + 9 + 9 + 7 + 241 + 366 + 9 + 9 + 6 + 8 = 666.

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (29972413669963) by changing a digit.

It is a polite number, since it can be written in 383 ways as a sum of consecutive naturals, for example, 69220354680 + ... + 69220355112.

It is an arithmetic number, because the mean of its divisors is an integer number (59632433280).

Almost surely, 2^{29972413669968} is an apocalyptic number.

29972413669968 is a gapful number since it is divisible by the number (28) 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 29972413669968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (57247135948800).

29972413669968 is an abundant number, since it is smaller than the sum of its proper divisors (84521858227632).

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

29972413669968 is a wasteful number, since it uses less digits than its factorization.

29972413669968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 678 (or 659 counting only the distinct ones).

The product of its digits is 3809369088, while the sum is 81.

The spelling of 29972413669968 in words is "twenty-nine trillion, nine hundred seventy-two billion, four hundred thirteen million, six hundred sixty-nine thousand, nine hundred sixty-eight".