105217968 has 60 divisors (see below), whose sum is σ = 280987224. Its totient is φ = 33926400.

The previous prime is 105217963. The next prime is 105217969. The reversal of 105217968 is 869712501.

It is a super-3 number, since 3×105217968³ (a number of 25 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is not an unprimeable number, because it can be changed into a prime (105217961) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 44988 + ... + 47268.

Almost surely, 2^105217968 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 105217968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (140493612).

105217968 is an abundant number, since it is smaller than the sum of its proper divisors (175769256).

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

105217968 is a wasteful number, since it uses less digits than its factorization.

105217968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2354 (or 2317 counting only the distinct ones).

The product of its (nonzero) digits is 30240, while the sum is 39.

The square root of 105217968 is about 10257.5810013862. The cubic root of 105217968 is about 472.0956188546.

The spelling of 105217968 in words is "one hundred five million, two hundred seventeen thousand, nine hundred sixty-eight".