100864963584 has 880 divisors, whose sum is σ = 398042916480. Its totient is φ = 24631050240.

The previous prime is 100864963579. The next prime is 100864963609. The reversal of 100864963584 is 485369468001.

100864963584 is a `hidden beast` number, since 10 + 0 + 8 + 6 + 49 + 6 + 3 + 584 = 666.

It is a super-2 number, since 2×100864963584² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a self number, because there is not a number n which added to its sum of digits gives 100864963584.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 108573232 + ... + 108574160.

It is an arithmetic number, because the mean of its divisors is an integer number (452321496).

Almost surely, 2^100864963584 is an apocalyptic number.

100864963584 is a gapful number since it is divisible by the number (14) 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 100864963584, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (199021458240).

100864963584 is an abundant number, since it is smaller than the sum of its proper divisors (297177952896).

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

100864963584 is a wasteful number, since it uses less digits than its factorization.

100864963584 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 996 (or 969 counting only the distinct ones).

The product of its (nonzero) digits is 4976640, while the sum is 54.

The spelling of 100864963584 in words is "one hundred billion, eight hundred sixty-four million, nine hundred sixty-three thousand, five hundred eighty-four".