105584394240 has 1008 divisors, whose sum is σ = 433221716088. Its totient is φ = 24461180928.

The previous prime is 105584394217. The next prime is 105584394337. The reversal of 105584394240 is 42493485501.

105584394240 is a `hidden beast` number, since 1 + 0 + 558 + 4 + 3 + 94 + 2 + 4 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 80311025664 + 25273368576 = 283392^2 + 158976^2 .

It is a super-2 number, since 2×105584394240² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 55 ways as a sum of consecutive naturals, for example, 6210846712 + ... + 6210846728.

Almost surely, 2^105584394240 is an apocalyptic number.

105584394240 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 105584394240, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (216610858044).

105584394240 is an abundant number, since it is smaller than the sum of its proper divisors (327637321848).

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

105584394240 is an frugal number, since it uses more digits than its factorization.

105584394240 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 87 (or 40 counting only the distinct ones).

The product of its (nonzero) digits is 691200, while the sum is 45.

The spelling of 105584394240 in words is "one hundred five billion, five hundred eighty-four million, three hundred ninety-four thousand, two hundred forty".