What is an irregular number?

Girl -- that's exactly what I was doing -- helping a student who reached out for help.

I was helping Makenzie who asked the original question. I didn't want her to think that your definition was right.

Do you mean an irrational number?

Or are you looking for an irregular prime number?

An irregular number is a real number that cannot be written as a simple fraction.

Example 3.14 or pie goes on and on and on.

Thank you! Haha I got confused between irregular and irrational

Girl Friday is wrong. She gave you the definition for an irrational number.

http://www.mathsisfun.com/irrational-numbers.html

An irregular number, also known as a non-harmonic number, is a positive integer that cannot be expressed as the sum of distinct divisors of itself. In other words, for an irregular number, there is no way to break it down into a sum of its divisors (excluding the number itself).

To determine if a number is irregular, you can follow these steps:

1. Find the divisors of the number: Start by listing out all the positive divisors of the number. These are the numbers that divide the original number evenly, leaving no remainder.

2. Check for distinct sums: Take all the possible combinations of the divisors (excluding the number itself), and calculate their sums. Make sure each sum is unique and does not equal the original number.

If you find at least one unique sum among all combinations, then the number is not irregular. However, if there is no distinct sum, then the number is irregular.

For example, let's consider the number 12:

The divisors of 12 are 1, 2, 3, 4, 6, and 12.

Possible combinations of divisors to check for distinct sums:

- 1 + 2 + 3 + 4 + 6 = 16
- 1 + 2 + 3 + 4 + 12 = 22
- 1 + 2 + 3 + 6 + 12 = 24
- 1 + 2 + 4 + 6 + 12 = 25
- 1 + 3 + 4 + 6 + 12 = 26

In this case, all the sums are distinct and none of them equal 12. Therefore, 12 is an irregular number.

Note: The concept of irregular numbers is not as commonly discussed or used as some other number classifications like prime, composite, or even perfect numbers.

MS.Sue do you always have to be so mean and add to others conversations? We need good tutors not someone to always put us down. Please don't do this to kids who are reaching out for help.