Introduction to Multiples

Being one of the most exciting chapters of mathematics, Multiples and Factors enables students to get into the fundamentals of calculating and simplifying equations. The chapter establishes a base for students which they can make use of while understanding more difficult areas of this subject. The chapter mainly contains the definition of multiples, how these are important in Mathematics, activity based on common factors and common multiples, etc., along with some examples.


The chapter also contains a detailed description and usage of factors and the differences between common factors and common multiples. These two are vital concepts related to each other; therefore, students should go through both these topics simultaneously to better understand them.


What are Multiples?

A multiple is a number that you get by multiplying other numbers together. And, multiples are a set of numbers where you have a base number that has been multiplied by other natural numbers.

In simpler terms, the multiples are obtained by multiplying one whole number with other numbers. Class 6 maths common factors and common multiples worksheets are the best resource students can go through to get hold of both Multiples and Factors. However, another better way to understand these series is by looking at the multiplication table, and the following are some multiples of natural numbers you can refer to.

You can go through the multiples of 3 for instance, 

3 x 0 = 0

3 x 1 = 3

3 x 3 = 9

3 x 4 = 12

Here, you can see that the multiples of 3 are 0, 3, 6, 9, 12, and the list is never-ending. Since any number can be multiplied with any other number, it inevitably has an infinite number of multiples. To delve deeper regarding the basics of Multiples, students should consider going through the worksheet of common multiples and factors for class 5th.


What is a Factor?

Factors can be specified as whole numbers that can evenly divide another number. Precisely, when a number is considered as a factor of another second number, the first one has to divide the second number completely without keeping any remainder behind.

In other words, if the dividend is evenly divisible by a number or also called as a divisor, that particular divisor will be known as a factor of that dividend. Every number is supposed to have a common factor, such as one (1) and also the number itself. The highest common factor and lowest common multiple TNPSC questions generally include questions related to these; therefore, students need to go through a few examples to comprehend them.

For instance,

4 is considered as a factor of 24, as it divides 24 evenly and leaves 6 as quotient and zero (0) as remainder. On the other hand, 6 is also considered as the factor of 24, which leaves 4 as quotient and zero (0) as remainder.

Consequently, it is apparent that 24 has multiple factors, such as 1, 24, 4, 6, and 2, 3, 8, including 12, since all these numbers can divide 24 evenly without leaving any remainder.


As discussed earlier, the factor is a number that generally keeps no remainder behind after dividing a particular number. On the other hand, multiple is a number obtained by multiplying a whole number by some other numbers. Following is a list of key differences between common factors and multiples class 4:


Difference Between Common Factors and Common Multiples

Comparison Factor

Multiples

Factors

Definition

Multiples are a result, obtained when a whole number gets multiplied by another number.

Factors can be referred to as an exact divisor of a specific number.

Outcome

It has to be equal or greater than a particular number.

It can be less than or similar (equal) to a particular number.

Number of factors/ multiples

Infinite

Finite

Operation used

Multiplication

Division


Along with these differences, students should also be aware of the process of common factors and common multiples to compare them. Mathematics mainly deals with numbers and different operations, and factors and multiples are one of those kinds. The concepts are pretty basic and should be grasped properly to understand higher-level mathematics in a better way.


Furthermore, with assistance from e-learning platforms like Vedantu, one can elevate their knowledge of multiples. The model exam question papers, expert notes, along with online classes, and doubt clearing sessions, students can better their final exam preparations.

FAQs (Frequently Asked Questions)

1. What are Prime Numbers?

Ans. When natural numbers consist of two factors such as 1 and the integer itself, those numbers are called a prime number. For example, 2 can be considered as a prime number as it also has two factors such as 1 and 2. On the contrary, the factors of number 6 will be 1, 2, 3, and 6. Therefore, it cannot be considered a prime number but a composite number for multiple factors.


One should remember that 1 can be a natural number factor; however, it cannot be considered a prime or composite number. In order to understand this concept better, students can also make use of co-prime numbers highest common factor and lowest common multiple NCERT for further information.

2. What do you Mean by Factor Pairs?

Ans. When two numbers get multiplied together to obtain a specific result or product, those numbers are called factor pairs. For instance, in order to get the product of 8, the multiplication process can look like: 2 x 4 and 1 x 8, in that case, the factor pairs for 8 have to be 2, 4, and 1, 8.


Most often, factors are given as pairs of numbers, and by multiplying them together, you get the original number. There are highest common factor and lowest common multiple calculators that students can use to calculate factor pairs or find out the highest and lowest among them.

3. Are the Highest Common Factors and Lowest Common Multiple Questions Available Online?

Ans. Factors and Multiples chapter comprises two key concepts that should be studied together to understand the basics and further dive deeper. Even though the concepts are easily comprehensible, students should also refer to various study materials where the questions and answers are available to help them. From detailed definitions to finding the least common multiple and highest common factor, key differences between both factors and multiples including, examples are easily accessible from renowned education sites like Vedantu.


The explanations of factors and multiples might vary; however, students can easily compare and find the most straightforward explanation to quickly understand the topic. They can also find common factors and common multiples class 6 worksheets in these websites and an online calculator to practice numerical.