111264 has 48 divisors (see below), whose sum is σ = 312480. Its totient is φ = 34560.

The previous prime is 111263. The next prime is 111269. The reversal of 111264 is 462111.

111264 = T₂₄ + T₂₅ + ... + T₈₇.

111264 is nontrivially palindromic in base 7.

It is a tau number, because it is divible by the number of its divisors (48).

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is not an unprimeable number, because it can be changed into a prime (111263) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1794 + ... + 1854.

It is an arithmetic number, because the mean of its divisors is an integer number (6510).

2¹¹¹²⁶⁴ 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 111264, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (156240).

111264 is an abundant number, since it is smaller than the sum of its proper divisors (201216).

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

111264 is a wasteful number, since it uses less digits than its factorization.

111264 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 93 (or 85 counting only the distinct ones).

The product of its digits is 48, while the sum is 15.

The square root of 111264 is about 333.5625878302. The cubic root of 111264 is about 48.0970259643.

Adding to 111264 its reverse (462111), we get a palindrome (573375).

It can be divided in two parts, 1112 and 64, that added together give a triangular number (1176 = T₄₈).

The spelling of 111264 in words is "one hundred eleven thousand, two hundred sixty-four".