105180768 has 480 divisors, whose sum is σ = 421521408. Its totient is φ = 24883200.

The previous prime is 105180763. The next prime is 105180781. The reversal of 105180768 is 867081501.

It is a super-2 number, since 2×105180768² = 22125987914139648, which 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 not an unprimeable number, because it can be changed into a prime (105180763) by changing a digit.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 3392913 + ... + 3392943.

Almost surely, 2^105180768 is an apocalyptic number.

105180768 is a gapful number since it is divisible by the number (18) 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 105180768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (210760704).

105180768 is an abundant number, since it is smaller than the sum of its proper divisors (316340640).

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

105180768 is a wasteful number, since it uses less digits than its factorization.

105180768 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 88 (or 71 counting only the distinct ones).

The product of its (nonzero) digits is 13440, while the sum is 36.

The square root of 105180768 is about 10255.7675480678. The cubic root of 105180768 is about 472.0399755475.

The spelling of 105180768 in words is "one hundred five million, one hundred eighty thousand, seven hundred sixty-eight".