## Table of Contents

## Definition Of Integers

Integers are a set of natural numbers that include zero and negative natural numbers.

For example:…,-3,-2,-1,0, 1, 2, 3,…. We can write an integer as a product of prime numbers. Also we can find the HCF and LCM of two integers by first writing each one as a product of prime numbers.

The collection of integers is symbolized by Z, where Z stands for Zahlen, which means “to count.”

## Types of Integers

After understanding the Integers definition, let’s understand different types of Integers. There are 3 types of Integers, which are explained below:

- Positive integers (Z+)
- Negative Integers (Z-)
- Zero Integer (0)

##### Positive Integers:

Any number greater than zero is referred to as a positive number, and in this context, positive integers are counting numbers or natural numbers. It is represented by the symbol ‘Z+’. Positive integers are found on the number line to the right of zero.

As an example: Z+ = { 1, 2, 3,…,∞ }

##### Negative Integers:

Any number less than zero is considered a negative number, and the negative of natural numbers is referred to as a negative integer. They are denoted by the letter ‘Z-‘. The negative integers are on the number line to the left of zero.

For instance – Z- = {-∞,…,-3,-2,-1}

##### Zero Integer

Zero (0) is neither positive nor negative. It is referred to as a neutral number for a reason: it lacks the signs ‘+’ and ‘-‘.

**Important:** Negative integers are also known as the additive inverses of positive integers.

## Integers on a Number Line

### Video Explanation of Integers

#### FAQ: Integers Definition

**Q1. Is “0” an Integer?**

**Ans.** No, Zero is not an Integer, it is a neutral number.

**Q2. Is a decimal number, say 1.5, an Integer?**

**Ans.** An integer, also known as a “round number” or “whole number,” is any positive or negative number that does not contain any decimal or fractional parts. For example, 3, -10, and 59 are Integers but 1.5, -46.2, 4/9, and 2/3 are not Integers.

**Q3. Are Integers also Rational Numbers?**

**Ans.** Yes, any integer can be converted cleanly into a fraction and is a rational number.

**Q4. Is every Integer a Real Number?**

**Ans.** Integers are real numbers, but not all real numbers are integers. Here are some examples of distinctions: Real numbers include integers as well as rational, irrational, whole, and natural numbers.

**Q5. Are Square Roots Integers?**

**Ans.** Integers are the square roots of perfect squares (e.g., 0, 1, 4, 9, 16). In all other cases, positive integer square roots are irrational numbers with non-repeating decimals in their decimal representations.

Like Integers definition, if you want to know about the Definition of natural numbers, then please check this article –**What are Natural Numbers?**