105663564 has 72 divisors (see below), whose sum is σ = 286322400. Its totient is φ = 32769792.

The previous prime is 105663563. The next prime is 105663611. The reversal of 105663564 is 465366501.

105663564 is a `hidden beast` number, since 1 + 0 + 566 + 35 + 64 = 666.

It is a super-2 number, since 2×105663564² = 22329577514364192, which contains 22 as substring.

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

It is not an unprimeable number, because it can be changed into a prime (105663563) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 28912 + ... + 32360.

It is an arithmetic number, because the mean of its divisors is an integer number (3976700).

Almost surely, 2^105663564 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 105663564, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (143161200).

105663564 is an abundant number, since it is smaller than the sum of its proper divisors (180658836).

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

105663564 is a wasteful number, since it uses less digits than its factorization.

105663564 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3519 (or 3514 counting only the distinct ones).

The product of its (nonzero) digits is 64800, while the sum is 36.

The square root of 105663564 is about 10279.2783793416. The cubic root of 105663564 is about 472.7611187933.

It can be divided in two parts, 1056 and 63564, that added together give a triangular number (64620 = T₃₅₉).

The spelling of 105663564 in words is "one hundred five million, six hundred sixty-three thousand, five hundred sixty-four".