105013814400 has 1728 divisors, whose sum is σ = 460360892160. Its totient is φ = 22560768000.

The previous prime is 105013814341. The next prime is 105013814407. The reversal of 105013814400 is 4418310501.

It is a happy number.

105013814400 is a `hidden beast` number, since 10 + 501 + 3 + 8 + 144 + 0 + 0 = 666.

It is a super-2 number, since 2×105013814400² (a number of 23 digits) contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (105013814407) by changing a digit.

It is a polite number, since it can be written in 215 ways as a sum of consecutive naturals, for example, 2838211182 + ... + 2838211218.

Almost surely, 2^105013814400 is an apocalyptic number.

105013814400 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 105013814400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (230180446080).

105013814400 is an abundant number, since it is smaller than the sum of its proper divisors (355347077760).

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

105013814400 is a wasteful number, since it uses less digits than its factorization.

105013814400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 143 (or 106 counting only the distinct ones).

The product of its (nonzero) digits is 1920, while the sum is 27.

The spelling of 105013814400 in words is "one hundred five billion, thirteen million, eight hundred fourteen thousand, four hundred".