101689216512000 has 1664 divisors, whose sum is σ = 370834799462400. Its totient is φ = 24594953011200.

The previous prime is 101689216511989. The next prime is 101689216512041. The reversal of 101689216512000 is 215612986101.

It is a tau number, because it is divible by the number of its divisors (1664).

It is a super-2 number, since 2×101689216512000² (a number of 29 digits) contains 22 as substring.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 511001087901 + ... + 511001088099.

It is an arithmetic number, because the mean of its divisors is an integer number (222857451600).

Almost surely, 2^{101689216512000} is an apocalyptic number.

101689216512000 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 101689216512000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (185417399731200).

101689216512000 is an abundant number, since it is smaller than the sum of its proper divisors (269145582950400).

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

101689216512000 is a wasteful number, since it uses less digits than its factorization.

101689216512000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 574 (or 542 counting only the distinct ones).

The product of its (nonzero) digits is 51840, while the sum is 42.

The spelling of 101689216512000 in words is "one hundred one trillion, six hundred eighty-nine billion, two hundred sixteen million, five hundred twelve thousand".