105416942400 has 2016 divisors, whose sum is σ = 501335690240. Its totient is φ = 21076070400.

The previous prime is 105416942347. The next prime is 105416942419. The reversal of 105416942400 is 4249614501.

105416942400 is a `hidden beast` number, since 1 + 0 + 54 + 169 + 42 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (2016).

It is a super-2 number, since 2×105416942400² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 1573387167 + ... + 1573387233.

Almost surely, 2^105416942400 is an apocalyptic number.

105416942400 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 105416942400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (250667845120).

105416942400 is an abundant number, since it is smaller than the sum of its proper divisors (395918747840).

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

105416942400 is a wasteful number, since it uses less digits than its factorization.

105416942400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 170 (or 138 counting only the distinct ones).

The product of its (nonzero) digits is 34560, while the sum is 36.

The spelling of 105416942400 in words is "one hundred five billion, four hundred sixteen million, nine hundred forty-two thousand, four hundred".