Class 4 Maths Multiples and Factors Complete Chapter

Hello students, welcome to our channel learning notebook. In today's video, we are going to do complete chapter of multiples and factors for class 4. We are going to cover each and every concept related to this chapter. So make sure you watch the entire video. But before starting with this video, let me tell you that we have made videos on every chapter of class 4 mathematics. We also have interesting worksheets and quizzes on each chapter. You can find all of them on our channel learning notebook. Also you can see list of all such videos on our website. The link to our website is below in the description box. So let's see what all topics we are going to cover today in this video. First we are going to understand what are multiples. Then we will learn about properties of multiples. How to find multiples of number. What are common multiples and how to find common multiples. Then we will understand what are factors, properties of factors, how to find factors of number, what are common factors and how to find common factors. Then students in the end will give you practice worksheet. So let's start and first understand what are multiples. The product of two or more numbers is the multiples of the numbers that are being multiplied. Let's understand it with the help of an example. 6 * 5 = to 30. So here the product 30 is the multiple of 6 and it is also the multiple of 5. Let's take another example. 2 into 4 into 5 = to 40. Here product 40 is the multiple of two. it is the multiple of four and 40 is also the multiple of five. So remember that the product of two or more numbers is the multiples of the numbers that are being multiplied. Students, let's consider the table of two here. 2 4 6 8 10 and so on. All these are multiples of 2. Similarly, in the table of four, 4 8 12 16 20 and so on. All these are multiples of four. Now the question is is there an end to multiples of number? Answer is there is no end to the multiples of number. Look here in this table of two. If we multiply 2 by 10, we get 20. If we multiply 2 by 20, we get 40. And then if we multiply 2 by 30, we get 60 and so on. So students, there is no end to the multiples of number. Now let's understand properties of multiples. First property of multiples is every number is multiple of one and multiple of itself. For example, 5 * 1 equals to 5. So here multiple five is multiple of 1 and it is also the multiple of itself that is five. Next 7 * 1 = to 7. So here 7 is multiple of 1 as well as multiple of itself that is seven. Now the next property of multiples is the smallest multiple of number is the number itself. Here students you can see multiples of two up to 80 but the smallest multiple of two is the number itself that is two. So this is the second property of multiple that is the smallest multiple of number is the number itself. Next property of multiples is every multiple of number is equal to or greater than the number. Let's again consider multiples of two. Here students you can see every multiple of two is either equal to two or greater than two. So remember that the multiple of number can never be less than the number. Now the next property is the multiples of number are endless. Thus there is no greatest multiple of number. Students this is the same property which we have learned earlier. So remember the multiples of number are infinite. There is no end to the multiples of number. Last property of multiples is multiple of number is divisible by the number. To understand this property let's consider multiples of three. So here we have 3 6 9 12 and so on. Let's pick number 36 which is multiple of 3. Now let's check if 36 is divisible by 3. On dividing we see that remainder is zero. So it means 36 which is the multiple of 3 is divisible by 3. So students these were the properties of multiples. Now let's revise these properties of multiples with the help of an exercise. Fill in the blanks. Question one is the smallest multiple of 13 is dash. Answer is 13 because we learned the property that the smallest multiple of number is the number itself. Question two is every number is multiple of dash and dash. Answer is itself and one. Next question is the first multiple of seven is dash. Answer is seven. Again with the reference to the property that the smallest or we can say first multiple of number is the number itself. Question four is the first three multiples of 8 are dash. For this we will do 8 into 1 = 8. Next 8 into 2 = 16 and 8 into 3 = 24. And the last question is 6 into 9 = to 54. So 54 is multiple of dash and dash. Answers are 6 and 9. Now let's understand how to find multiples. To find multiples of number, multiply the number by 1 2 3 4 5 and so on. Students, let's understand it with the help of an example. Find the first five multiples of seven. To find first five multiples of seven, we will multiply seven with 1 2 3 4 and 5. So first five multiples of 7 are 7 14 28 and 35. Now let's see the next question. Find the first five even multiples of three. Students, to get even multiples, we cannot multiply the number by 1 2 3 and so on. because in this way we will get even as well as odd multiples. Now if you notice carefully you will see that on multiplying any number by an even number we always get the multiple as an even number. So here also we will multiply three with even numbers like 2 4 6 8 and 10. So in this way we have found the first five even multiples of three which are 6 24 and 30. Let's do one more question. Find the first five odd multiples of 9. So here students to find first five odd multiples of 9 let's multiply 9 by first five odd numbers that is 1 3 5 7 and 9. So we have got the first five odd multiples of 9 which are 9 27 63 and 81. Now let's take one more example. Find the first five odd multiples of four. Now students told you that to find odd multiples of any number we will multiply the number by odd numbers. So let's multiply four by 1 3 5 7 and 9. Now if you notice here none of the multiple is an odd number. So it means if the number is even then all its multiples are always even. We can never get odd multiples of an even number. So here our answer would be there are no odd multiples of four. So students, this was all about multiples, properties of multiples and how to find multiples. Now let's see how to find common multiples. So what are common multiples? number that is multiple of two or more numbers is called common multiple. For this let's consider multiples of four and multiples of five. Students look at these multiples carefully. You will find that 20 is multiple of both four as well as five. Therefore, 20 is common multiple of 4 and 5. Similarly, 40. 40 is multiple of both. 4 as well as five. So, 40 is also common multiple of four and five. Now let's do question on common multiples. Find the first 10 multiples of 2 and three to find their common multiples. So let's write first 10 multiples of two as well as first 10 multiples of three. So here students we can see that six is the first common multiple of 2 and 3. Then let's check further. Now we can see 12. 12 is another common multiple of 2 and 3. Let's check further. We can see 18. 18 is also common multiple of 2 and 3. So let's write the answer. Common multiples of 2 and 3 are 6, 12 and 18. Now let's understand what are factors. When two or more numbers are multiplied, each of the number being multiplied is called the factor. Let's consider few examples. 3 * 7 equals to 21. So here students we have learned that 21 is multiple of 3 and 7. Also 3 and 7 are factors of 21. Let's take one more example. 2 into 3 into 5 = 30. So 30 is multiple of 2 3 and 5. And remember that 2 3 and five are factors of 30. So when two or more numbers are multiplied, each of the number being multiplied is called the factor. In other words, we can say factors are the numbers which divide the given number completely. That is remainder equals to zero. For example, if we divide 30 by factor 6, we get the remainder as zero. And if we divide 30 by factor 5 then also we get the remainder as zero. Now let's learn the properties of factors. First property of factors is one is factor of all numbers. For example, 20 into 1 equals to 20. So here 1 is factor of 20. Next example is 13 into 1 equals to 13. So 1 is factor of 13. So students remember that one is factor of all the numbers. Also students one is the smallest factor of any given number. Now next property of factors is number is factor of itself. Like in earlier examples, 20 is factor of 20 itself and 13 is factor of 13 itself. Now let's see the next property of factors. number itself is the greatest factor of itself. For example, 20 into 1 = 20. So here 20 is the greatest factor of 20. Similarly 13 into 1 equals to 13. So 13 is the greatest factor of 13 itself. Now next property is the factor of number is smaller than or equal to the number. For example, factors of 14 are 1 2 7 and 14. So students here among all the factors of is the highest which is equal to number 14 and all other factors are smaller than number 14. And the last property of factors is every number has at least two factors that is 1 and itself. For example, 14 into 1 equals to 14. So 14 has at least two factors 1 and 14 itself. So these were the properties of factors. Now let's revise properties of factors with the help of an exercise. Fill in the blanks. First question is 4 * 7 = 28. Therefore 4 and 7 are factors of dash. Answer is 28. Next question is 5 * 6 = 30. Therefore factors of 30 are dash and dash. Answers are five and six. Next, the smallest factor of 20 is dash. Answer is one because we learn the property that one is the smallest factor of number. Let's see the next question. Dash is factor of all the numbers. Answer is one. One is factor of all numbers. Let's see the next question. Dash is the biggest factor of 80. Answer is 80. Because we learn the property that number itself is the greatest or biggest factor of itself. Now the last question is dash has only one factor. Answer is one. Number one has only one factor that is itself. Now let's learn how to find factors using multiplication and division. Let's first understand how to find factors using multiplication. Question is find the factors of 24. Students to find factors of 24 we will start writing from table of 1. 1 into 24 = 24. In the table of 2, 2 into 12 = 24. In the table of three, 3 into 8 = 24. Similarly, in the table of 4, 4 into 6 = 24. Now students 24 does not come in the table of five or we can say 24 is not divisible by 5 and in the table of 6 6 into 4 equals to 24. But we have already covered it as 4 into 6 = 24. So it means we have to stop at 4 into 6. Now we have found all the factors of 24. So let's start writing its factors. We will start writing from top to bottom. 1 2 3 4. And now we will start writing from bottom to top. 6 8 12 and 24. So students in this way we have found the factors of 24. Let's do one more question. Find the factors of 30. Again to find factors of 30, we will start writing from table of 1. 1 into 30 = to 30. In the table of 2, 2 into 15 = 30. In the table of three, 3 into 10 equals to 30. Now 30 does not come in the table of four or we can say 30 is not divisible by 4. Now in table of five, 5 into 6 equals to 30. And in the table of 6, 6 into 5 = to 30. But students, we have already covered it as 5 into 6 = to 30. So it means we have to stop here. So now we have found all the factors of 30. So let's start writing its factors. We will start from top to bottom. 1 2 3 5 and then we will write from bottom to top. 6 10 15 and 30. So we have found the factors of 30. So students in this way you can find the factors of any number using multiplication. Now let's see how to find factors of number using division. Question is find the factors of 18 using division. To find factors using division, we will divide number by 1 2 3 and so on. So to find factors of 18, let's first divide 18 by 1. We get remainder equals to zero. So 1 and 18 are factors of 18. Now we will divide 18 by 2 and again we get remainder equals to 0. So 2 and 9 are also factors of 18. Next let's divide 18 by 3. Again we get remainder equals to zero. Therefore 3 and 6 are also factors of 18. Now students we will divide 18 by 4. Here we get remainder equals to 2. So it means 4 is not the factor of 18. Now let's divide 18 by 5. We get remainder equals to 3. So it means 5 is also not factor of 18. Next divide 18 by 6. We get remainder equals to 0. And thus we get 3 and six as factors of 18 but we have already got these two factors. So it means we will stop here and won't divide further. So let's write factors of 18 now which are 1 2 6 9 and 18. Students, to find factors of number, we generally use multiplication method. But division method is used to find if particular number is factor of another number or not. So let's solve such question. Find out if three is factor of 45. To find out if 3 is factor of 45, we will divide 45 by 3. And if we get remainder as zero, then we can say that yes, 3 is factor of 45. So let's divide 3 * 1 = 3. 4 - 3 = 1. Copy five. and then 3 * 5 = to 15 and 15 - 15 = to 0. So here we have got the remainder as 0. So it means 3 is factor of 45. Now our next topic is common factors. So what is common factor? number that is factor of two or more numbers is called common factor. Let's see some examples. Two is common factor of six as well as 8. Similarly, three is common factor of 9 as well as 15. Now let's see how to find common factors. Question is find all the factors of 20 and 32 and then find their common factors. First let's find factors of 20. For this we will start writing table of 1. 1 into 20 equals to 20. In the table of 2, 2 into 10 = 20. Now 20 is not divisible by 3. And in the table of four, 4 into 5 equals to 20. And in the table of five, 5 into 4 = to 20. But we have already covered it as 4 into 5. So we will stop at 4 into 5. So let's write factors of 20 which are 1 2 4 then 5 10 and 20. Now let's find factors of 32. In the table of 1, 1 into 32 = 32. In the table of 2, 2 into 16 equals to 32. 32 is not divisible by 3. Then in the table of 4, 4 into 8 equals to 32. Then 32 is not divisible by 5, 6 or 7. And in table of 8 8 into 4 equals to 32. But we have just covered it as 4 into 8. So let's stop here. So factors of 32 are 1 2 4 8 16 and 32. So now we have found the factors of 20 as well as factors of 32. Now students what are common factors of 20 and 32? Let's see. Common factors are 1 2 and 4. So let's write common factors of 20 and 32 are 1 2 and 4. So students this is how we can find common factors of given numbers. Now in the end I'm giving you worksheet for your practice. So students, this worksheet contains questions from all the sections of the chapter which have just taught to you. If you have skipped any of the section, will suggest you to first understand it and then attempt this worksheet. Do watch my other videos and share my channel and my video with your friends and family. Thanks for watching. See you in the next video. Bye-bye.