105312054450240 has 1344 divisors, whose sum is σ = 414762899362560. Its totient is φ = 25131434803200.

The previous prime is 105312054450227. The next prime is 105312054450241. The reversal of 105312054450240 is 42054450213501.

105312054450240 is a `hidden beast` number, since 1 + 0 + 5 + 3 + 1 + 20 + 544 + 50 + 2 + 40 = 666.

It is a super-2 number, since 2×105312054450240² (a number of 29 digits) contains 22 as substring.

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

It is a junction number, because it is equal to n+sod(n) for n = 105312054450195 and 105312054450204.

It is not an unprimeable number, because it can be changed into a prime (105312054450241) by changing a digit.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 52735128922 + ... + 52735130918.

It is an arithmetic number, because the mean of its divisors is an integer number (308603347740).

Almost surely, 2^{105312054450240} is an apocalyptic number.

105312054450240 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 105312054450240, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (207381449681280).

105312054450240 is an abundant number, since it is smaller than the sum of its proper divisors (309450844912320).

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

105312054450240 is a wasteful number, since it uses less digits than its factorization.

105312054450240 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2809 (or 2782 counting only the distinct ones).

The product of its (nonzero) digits is 96000, while the sum is 36.

The spelling of 105312054450240 in words is "one hundred five trillion, three hundred twelve billion, fifty-four million, four hundred fifty thousand, two hundred forty".