Chapter 3

Playing with Numbers

Introduction

Understanding the number system is essential to have an excellent concept of mathematics. So, we need to begin at a very early age in our education and have a crystal clear knowledge of the (maths class 6 chapter 3) numbers to understand its applications in various fields. Now let us take an example to understand how to arrange trees in a garden, considering that having the same number of trees in each row is equal to the number of rows in the garden.

Rahul had 36 trees and wanted to plant these 36 trees in the garden in a certain number of rows and columns. He desires to arrange them in rows so that each row has the same number of trees. He arranges them in the following ways and matches the total number of trees.

1- Trees in each row is 2, and the number of rows is 18, then, Total number of trees = 2 × 18 = 36 

2- Trees in each row is 3, and the number of rows is 12, then, Total number of trees = 3 × 12 = 36

3- Trees in each row is 4, and the number of rows is 9, then, Total number of trees = 4 × 9 = 36

4- Trees in each row is 6, and the number of rows is 6, then, Total number of trees = 6 × 6 = 36

After making 4 different types of arrangements, we conclude that if we have 6 trees in each row and the number of rows is also six, then the product of the number of trees in each row and number of rows come out to be 36. We can see here that we are also arriving at a concept of a perfect square which means that if the exact number is multiplied by itself, then we obtain a square of that number. To get more such exciting examples, please Download the MSVgo app for free and learn with enjoyment by joining the intelligent community of educators and learners.

A similar example can be taken where we need to find all the factors of the number 20. For this, we need to learn the tables till 20 to solve such types of questions quickly.

1*20=20, 2*10=20, 4*5=20, Further if we make factors, it's just the repetition of the same numbers; therefore, the factors of the number 20 are 1, 2, 4, 5, 10, and 20. We can also conclude that the number 20 has 6 factors. To get more such interesting examples, play the MSVgo app for free and learn with the intelligent community of MSVgo Interschool Challenge.

Now let's move to another example, and in this question, we need to find all the factors of the number 36. The answer is 1*36=36, 2*18=36, 3*12=36, 4*9=36, 6*6=36. Further, if we make factors, it's just the repetition of the same numbers; therefore, the factors of the number 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. We can also conclude that the number 36 has 9 factors.

The next question is to find the first 5 multiples of 9. So basically, we should know the table of 9, and it will be beneficial to solve this question with the use of the table. The answer is, 9*1=9, 9*2=18, 9*3=27, 9*4=36, 9*5=45. So the required multiples are 9, 18, 27, 36, and 45.

A prime number is defined as a number that is divisible by 1 and by itself. There are 25 prime numbers between 1 to 100. The list of prime numbers from 1 to 100 is as follows- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. It should be noted that 1 is neither a prime nor a composite number. On the other hand, Composite numbers are those numbers that have more than two factors. 

Divisibility test for 2:- For any number to be divisible by 2, the last digit of that particular number should be 0, 2,4, 6, or 8. For example, 76 is completely divisible by 2 because the number's last digit is 6, i.e., an even number.

Divisibility test for 3:- For any number to be divisible by 3, the sum of the digits of that particular number should be completely divisible by 3. It can also be said that if the sum of digits of a specific number is a multiple of 3, it is also completely divisible by 3. Let's take some examples to understand it. 287 is not divisible by 3 because the sum of digits of the number 287 is 2+8+7=17, and 17 is not completely divisible by 3; therefore, the number 287 is also not divisible by 3. 285 is divisible by 3 because the sum of digits of the number 285 is 2+8+5=15, and 15 is completely divisible by 3; therefore, the number 285 is also divisible by 3.

Divisibility test for 4:- For any number to be divisible by 4, the last two digits of that particular number should be completely divisible by 4. Let's take some examples to understand it. 23744 is divisible by 4 because the last two digits of the number 23744 are completely divisible by 4. Join the MSVgo app for free and learn with the intelligent community of educators, learners, and MSVgo Interschool Challenge to get more interesting examples.

Divisibility test for 6:- For any number to be completely divisible by 6, the number should be divisible by both 2 and 3. For example, 42 is completely divisible by 6 because the number is completely divisible by both 2 and 3.

Divisibility test for 8:- For any number to be divisible by 8, the last three digits of that particular number should be completely divisible by 8. Let's take some examples to understand it. 547832 is divisible by 8 because the last three digits of 547832 are completely divisible by 8.

Divisibility test for 9:- For any number to be divisible by 9, the sum of the digits of that particular number should be completely divisible by 9. It can also be said that if the sum of digits of any particular number is a multiple of 9, it is also completely divisible by 9. Let's take some examples to understand it. 217 is not divisible by 9 because the sum of digits of the number 217 is 2+1+7=10, and 10 is not completely divisible by 9; therefore, the number 217 is also not divisible by 9. 288 is divisible by 9 because the sum of digits of the number 288 is 2+8+8=18, and 18 is completely divisible by 9; therefore, the number 288 is also divisible by 9.

Divisibility test for 5:- For any number to be divisible by 5, the last digit of that particular number should be either 0 or 5. For example, 490 is completely divisible by 5 because the number's last digit is zero. 

Divisibility test for 10:- For any number to be divisible by 10, the last digit of that particular number should be 0. For example, 6190 is completely divisible by 10 because the number's last digit is zero. To get more such interesting examples, play the MSVgo app for free and learn with the intelligent community of the msvgo Interschool Challenge.

The article is beneficial for the students to improve their problem-solving speed, receive higher grades, and master the subject with frequent practice. Students must grasp mathematical concepts early in their academic careers. Students can use this method to lay a solid foundation for the subject. The article is meant to make studying the topics easy for students. Also, Class 6 Playing With Numbers is significant for understanding the number system as it is used throughout mathematics, physics, and in every aspect of the numerical and quantitative aptitude domain. So, a crystal clear concept and understanding of the topic is required at an early stage of education.

So, try to play on the MSVgo app - for games & msvgo Interschool Challenge to have a fantastic learning experience.

Other Courses

Related Chapters