105415261920 has 768 divisors, whose sum is σ = 424656691200. Its totient is φ = 24246190080.

The previous prime is 105415261907. The next prime is 105415261949. The reversal of 105415261920 is 29162514501.

105415261920 is a `hidden beast` number, since 1 + 0 + 5 + 4 + 15 + 2 + 619 + 20 = 666.

It is a super-2 number, since 2×105415261920² (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 pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 43254942 + ... + 43257378.

It is an arithmetic number, because the mean of its divisors is an integer number (552938400).

Almost surely, 2^105415261920 is an apocalyptic number.

105415261920 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 105415261920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (212328345600).

105415261920 is an abundant number, since it is smaller than the sum of its proper divisors (319241429280).

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

105415261920 is a wasteful number, since it uses less digits than its factorization.

105415261920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2528 (or 2514 counting only the distinct ones).

The product of its (nonzero) digits is 21600, while the sum is 36.

The spelling of 105415261920 in words is "one hundred five billion, four hundred fifteen million, two hundred sixty-one thousand, nine hundred twenty".