101116814400 has 672 divisors, whose sum is σ = 443463680000. Its totient is φ = 21894727680.

The previous prime is 101116814377. The next prime is 101116814429. The reversal of 101116814400 is 4418611101.

101116814400 is a `hidden beast` number, since 101 + 116 + 8 + 1 + 440 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (672).

It is a super-2 number, since 2×101116814400² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 5736801 + ... + 5754399.

Almost surely, 2^101116814400 is an apocalyptic number.

101116814400 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 101116814400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (221731840000).

101116814400 is an abundant number, since it is smaller than the sum of its proper divisors (342346865600).

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

101116814400 is a wasteful number, since it uses less digits than its factorization.

101116814400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 17656 (or 17635 counting only the distinct ones).

The product of its (nonzero) digits is 768, while the sum is 27.

The spelling of 101116814400 in words is "one hundred one billion, one hundred sixteen million, eight hundred fourteen thousand, four hundred".