105072 has 40 divisors (see below), whose sum is σ = 297600. Its totient is φ = 31680.

The previous prime is 105071. The next prime is 105097. The reversal of 105072 is 270501.

It is a happy number.

It is a super-2 number, since 2×105072² = 22080250368, which contains 22 as substring.

It is an Ulam number.

It is an alternating number because its digits alternate between odd and even.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (105071) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 429 + ... + 627.

It is an arithmetic number, because the mean of its divisors is an integer number (7440).

2¹⁰⁵⁰⁷² is an apocalyptic number.

105072 is a gapful number since it is divisible by the number (12) 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 105072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (148800).

105072 is an abundant number, since it is smaller than the sum of its proper divisors (192528).

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

105072 is a wasteful number, since it uses less digits than its factorization.

105072 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 221 (or 215 counting only the distinct ones).

The product of its (nonzero) digits is 70, while the sum is 15.

The square root of 105072 is about 324.1481142935. The cubic root of 105072 is about 47.1877206399.

Adding to 105072 its reverse (270501), we get a palindrome (375573).

The spelling of 105072 in words is "one hundred five thousand, seventy-two".