HOW THE FACTS RELATED TO TYPES OF NUMBERS FOLLOW SOME RULES?

1.INTRODUCTION

There are different types of numbers like whole numbers, natural numbers, real numbers, etc. Natural numbers are further divided into odd numbers and even numbers. Odd numbers are not divided by 2, whereas even do. Further prime and composite numbers are quite similar to odd and even numbers with some exceptional cases. In this article, various facts related to them will be discussed along with some practical rules.

2.FACTS RELATED TO NATURAL NUMBER 1

Other than 0,1, the only natural number whose square, square root, cube, and cube root are equal to the number itself. (Note: here the square roots considered only the positive ones, not negative)
When 1 is subtracted from an odd number, it results in an even number and subtraction from even results in the odd number. For example, 41-1=40 and 70-1=69.
When 1 is added to an odd number, it results in an even number, and add to an even number results in an odd number.For example 126+1=127 and 43+1=44.

2.FACTS RELATED TO EVEN AND ODD NUMBERS

The facts related to odd and even numbers can be summarised under a table as follows;

ODD + EVEN	ODD NUMBER
EVEN +EVEN	EVEN NUMBER
ODD + ODD	EVEN NUMBER
*ODD ODD**	ODD NUMBER
*ODD EVEN**	EVEN NUMBER
*EVEN EVEN**	EVEN NUMBER

3.FACTS RELATED TO PRIME AND COMPOSITE NUMBERS

The sum of two prime numbers always results in a composite number, except a case of 2 and 3 whose sum results in 5, which is a prime too. Other than this, all result in a composite number.

The various facts related to them can be summarised under the table as follows:

PRIME + PRIME	COMPOSITE EXCEPT 2 AND 3
PRIME + COMPOSITE	COMPOSITE NUMBER
COMPOSITE + COMPOSITE	COMPOSITE NUMBER
*PRIME PRIME**	COMPOSITE NUMBER
*PRIME COMPOSITE**	COMPOSITE NUMBER
*COMPOSITE COMPOSITE**	COMPOSITE NUMBER
COMPOSITE-COMPOSITE	COMPOSITE NUMBER
PRIME - PRIME	COMPOSITE EXCEPT 2 AND 3 AS 1 IS NEITHER PRIME NOR COMPOSITE

4.FACTS RELATED TO CO-PRIME NUMBERS

Both have a common factor that is 1.

for example (2,3),(11,13) etc.

5.RELATIONSHIP BETWEEN ODD-EVEN AND PRIME-COMPOSITE NUMBERS

An even number is always a composite number, but a composite number need not be always even. For example, 360,450,786 are even as well as composite. But like 27,81,123 are odd numbers, but they are composite because they have more factors other than 1 like 3,9,27.123 has 3,1 and 41.
An odd number can be prime as well as composite too. For example, 11,19,17 are odd numbers, and they are prime as well. But 9,45,27,343,49, and many other numbers are odd, but they are composite too as they have other factors than 1.
Referring to checkpoint 1, only the even number 2 is prime and cannot be considered composite. Similarly, 1 is an odd number but is neither prime nor a composite one.
All even composite numbers are completely divisible by 2, but an odd composite number cannot be divided by 2, which will result in decimal results. For example, the number 51 is odd and composite but not divisible by 2.