101512417968 has 960 divisors, whose sum is σ = 359608983552. Its totient is φ = 27411333120.

The previous prime is 101512417967. The next prime is 101512417991. The reversal of 101512417968 is 869714215101.

101512417968 is a `hidden beast` number, since 1 + 0 + 1 + 512 + 4 + 1 + 79 + 68 = 666.

It is not an unprimeable number, because it can be changed into a prime (101512417961) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 985557405 + ... + 985557507.

Almost surely, 2^101512417968 is an apocalyptic number.

101512417968 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 101512417968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (179804491776).

101512417968 is an abundant number, since it is smaller than the sum of its proper divisors (258096565584).

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

101512417968 is a wasteful number, since it uses less digits than its factorization.

101512417968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 224 (or 206 counting only the distinct ones).

The product of its (nonzero) digits is 120960, while the sum is 45.

The spelling of 101512417968 in words is "one hundred one billion, five hundred twelve million, four hundred seventeen thousand, nine hundred sixty-eight".