106272 has 60 divisors (see below), whose sum is σ = 320166. Its totient is φ = 34560.

The previous prime is 106261. The next prime is 106273. The reversal of 106272 is 272601.

It is a happy number.

It can be written as a sum of positive squares in only one way, i.e., 104976 + 1296 = 324^2 + 36^2 .

It is a super-2 number, since 2×106272² = 22587475968, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is not an unprimeable number, because it can be changed into a prime (106273) by changing a digit.

106272 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 9 ways as a sum of consecutive naturals, for example, 2572 + ... + 2612.

2¹⁰⁶²⁷² is an apocalyptic number.

106272 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 106272, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (160083).

106272 is an abundant number, since it is smaller than the sum of its proper divisors (213894).

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

106272 is an equidigital number, since it uses as much as digits as its factorization.

106272 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 63 (or 46 counting only the distinct ones).

The product of its (nonzero) digits is 168, while the sum is 18.

The square root of 106272 is about 325.9938649729. The cubic root of 106272 is about 47.3666806378.

Adding to 106272 its reverse (272601), we get a palindrome (378873).

It can be divided in two parts, 106 and 272, that added together give a triangular number (378 = T₂₇).

The spelling of 106272 in words is "one hundred six thousand, two hundred seventy-two".