105672 has 64 divisors (see below), whose sum is σ = 328320. Its totient is φ = 27648.

The previous prime is 105667. The next prime is 105673. The reversal of 105672 is 276501.

It is a super-2 number, since 2×105672² = 22333143168, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (21).

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

It is not an unprimeable number, because it can be changed into a prime (105673) by changing a digit.

105672 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 2838 + ... + 2874.

It is an arithmetic number, because the mean of its divisors is an integer number (5130).

2¹⁰⁵⁶⁷² is an apocalyptic number.

105672 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 105672, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (164160).

105672 is an abundant number, since it is smaller than the sum of its proper divisors (222648).

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

105672 is a wasteful number, since it uses less digits than its factorization.

105672 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 70 (or 66 counting only the distinct ones).

The product of its (nonzero) digits is 420, while the sum is 21.

The square root of 105672 is about 325.0722996504. The cubic root of 105672 is about 47.2773699941.

It can be divided in two parts, 1056 and 72, that added together give a triangular number (1128 = T₄₇).

The spelling of 105672 in words is "one hundred five thousand, six hundred seventy-two".