105006012169680 has 320 divisors, whose sum is σ = 362287149638400. Its totient is φ = 27955189463040.

The previous prime is 105006012169657. The next prime is 105006012169691. The reversal of 105006012169680 is 86961210600501.

105006012169680 is a `hidden beast` number, since 1 + 0 + 500 + 6 + 0 + 1 + 2 + 1 + 69 + 6 + 80 = 666.

It is a super-2 number, since 2×105006012169680² (a number of 29 digits) contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 10164162115 + ... + 10164172445.

It is an arithmetic number, because the mean of its divisors is an integer number (1132147342620).

Almost surely, 2^{105006012169680} is an apocalyptic number.

105006012169680 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 105006012169680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (181143574819200).

105006012169680 is an abundant number, since it is smaller than the sum of its proper divisors (257281137468720).

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

105006012169680 is a wasteful number, since it uses less digits than its factorization.

105006012169680 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 17699 (or 17687 counting only the distinct ones).

The product of its (nonzero) digits is 155520, while the sum is 45.

The spelling of 105006012169680 in words is "one hundred five trillion, six billion, twelve million, one hundred sixty-nine thousand, six hundred eighty".