Education

Integers and Composite Numbers

What are Integers?

In Mathematics, integers are numbers that can be positive, negative, and zero. Integers can, although not be a fraction. These numbers are used to perform various numerical operations, like addition, subtraction, multiplication, and division. The examples of integers are, 1, 24, 5,8, -67, -12, etc. The symbol of integers is the capital letter “Z. “

In terms of sets of integers, they include zero, a set of whole numbers, a set of natural numbers that are also known as counting numbers and their respective inverses. Integers are subordinates of real numbers. 

Examples of integers are: -100,-12,-1, 0, 2, 1000, 9769 etc…

As a set, it can be shown as follows:

Z= {… -3, -2, -1, 0, 1, 2, 3,…}

Integers consist of the following types of numbers:

  • Real Numbers
  • Natural Numbers
  • Whole Numbers
  • Rational numbers
  • Irrational numbers
  • Even and Odd Numbers, etc.                     

Types of Integers

Integers are of three types:

  • Zero 

The number zero is neither a positive nor a negative integer. It is a neutral number. This is because zero has no sign. 

  • Positive Integers 

Positive integers are those numbers that are positive. Positive integers are represented by a plus sign. All positive integers lie on the right side of zero in a number line. Hence, all positive integers are greater than zero.

  • Negative Integers 

Negative integers are numbers represented with a minus sign. Negative integers are shown on the left side of zero on the number line.

What do you mean by Integers?

The word integer is derived from the Latin word “Integer,” which means whole. Integers are a special set of whole numbers composed of zero, positive numbers, and negative numbers. Integers are denoted by the letter Z.

Symbol of Integers

The integers are represented by the capital letter ‘Z.’ 

Z = {…-4,-3,-2,-1,0,1,2,3,4…}

Important Properties of Integers

The Fundamental Properties of Integers are:

  1. Closure Property
  2. Associative Property
  3. Commutative Property
  4. Distributive Property
  5. Additive Inverse Property
  6. Multiplicative Inverse Property
  7. Identity Property

What are Composite Numbers?

Composite numbers are numbers that have more than two factors divisible. All-natural numbers which are not prime numbers are composite numbers as they are divided by more than two numbers. For instance, 6 is a composite number because it is divisible by 1, 2, 3, and even 6, such as:

  • 6÷1 = 6
  • 6÷2 = 3
  • 6÷3 = 2
  • 6÷6 = 1

Ways to Determine Composite Number :

The easiest way to find whether a respective number is composite is by:

  • Finding all the factors of the positive integer
  • If they are a part of the number line

Types of Composite Numbers

There are two categories of composite numbers which are:

  • Odd Composite Numbers or Composite Odd Numbers

All the odd integers which are not prime numbers are odd composite numbers. Examples of odd composite numbers are 15, 21, 25, 27, 31, etc. Let us consider the numbers 1, 2, 3, 4, 9, 10, 11,12, and 15 . In this given set of numbers, only 9 and 15 are the odd composite numbers because those two numbers satisfy the composite number condition.

  • Even Composite Numbers or Composite Even Numbers

All the even integers which are not prime numbers are even composite numbers. Examples of even composite numbers are 4, 6, 10, 12, 14, 18, etc. The numbers set 1, 2, 3, 4, 9, 10, 11,12, and 15 have only 4, 10, and 12 as the even composites because only those two numbers follow the composite number conditions.

Fun facts

  • The smallest Composite Number is 4
  • The smallest Prime Number is 2
  • The smallest Odd Composite Number is 9
  • The two-digit Smallest Composite Number is 12

 

Conclusion 

Integers and composite numbers build an essential and solid foundation of mathematics. Solving Cyuemath worksheets can help you explore these topic in detail. Cuemath also conducts online classes for kids for various grades that can help kids learn from the comfort of their home. Cuemath helps student  prepare for advanced math and strengthen their academic grades.   

Piyushi

Blogger By Passion, Programmer By Love and Marketing Beast By Birth.

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