105212016000 has 2304 divisors, whose sum is σ = 501816107520. Its totient is φ = 20901888000.

The previous prime is 105212015893. The next prime is 105212016001. The reversal of 105212016000 is 610212501.

105212016000 is a `hidden beast` number, since 1 + 0 + 52 + 12 + 0 + 1 + 600 + 0 = 666.

It is a super-2 number, since 2×105212016000² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (105212016001) by changing a digit.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 2843567982 + ... + 2843568018.

It is an arithmetic number, because the mean of its divisors is an integer number (217802130).

Almost surely, 2^105212016000 is an apocalyptic number.

105212016000 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 105212016000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (250908053760).

105212016000 is an abundant number, since it is smaller than the sum of its proper divisors (396604091520).

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

105212016000 is a wasteful number, since it uses less digits than its factorization.

105212016000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 130 (or 98 counting only the distinct ones).

The product of its (nonzero) digits is 120, while the sum is 18.

Adding to 105212016000 its reverse (610212501), we get a palindrome (105822228501).

The spelling of 105212016000 in words is "one hundred five billion, two hundred twelve million, sixteen thousand".