 Hi and welcome to the session. Today we will learn about common factors and common multiples. So first of all let us learn what are the common factors. We will understand this with the help of example. So let us find out common factors of 6 and 20. For this we will first of all find the factors of 6 and factors of 20. So factors of 6 are 1, 2, 3 and 6 and the factors of 20 are 1, 2, 4, 5, 10 and 20. Now to find out the common factors of 6 and 20 we will find out those numbers which are the factors of both 6 and 20 these are 1. So that means 1 and 2 are the factors of both 6 and 20 that means these are the common factors of 6 and 20. Now let us see what are coplying numbers. Two numbers having only one as a common factor coplying numbers. Let us take an example for this. Factors are 1 and 2 and factors of 3 are 1 and 3. Now common factor of 2 and 3 is only 1. So that means 2 and 3 are coplying numbers. Now our next topic is common multiples. For this also we will take an example. Let us find out the common multiples of 2 and 3. So first of all let us find out the multiples of 2 these are 2, 4, 6, 8, 10, 12, 14, 16, 18 and so on. Now the multiples of 3 are 3, 6, 9, 12, 15, 18, 21 and so on. Now let us find out the numbers which are the multiples of 2 and 3 both. These are 6, 18 and so on. So that means 6, 12, 18 and so on are the multiples of both 2 and 3. So these are the common multiples. Now let us see some divisibility rules. First divisibility rule is if a number is divisible by another number then it is divisible by each of the factors of that number. For example 12 is divisible by 6. Now of 6 are 1, 2, 3 and 6 and we know that 12 is also divisible by 1, 2, 3 and 6. That means 12 which is divisible by 6 is also divisible by all the factors of 6. Now let us move on to second divisibility rule. If a number is divisible it is divisible by their product also. Let us take an example for this. We know that 2 and 3 are coplying numbers. 12 is divisible by both the product of 2 and 3 is 6 and we know that 12 is divisible by 6 as well. So that means 12 which is divisible by 2 coplying numbers is also divisible by their product that is 6. Now third divisibility rule is if two given numbers are divisible by a number then their sum is also divisible by that number. Let us take an example for this. 12 and 9 are both divisible by 3. Now 12 plus 9 is equal to 21 and we know that 21 is also divisible by 3. So that means two given numbers 12 and 9 are divisible by 3 then their sum 21 is also divisible by 3. Now fourth and last divisibility rule is if two given numbers are divisible by a number then their difference is also divisible by that number. We will take an example for this also. Now two numbers 15 and 9 are divisible by 3. Now their difference 15 minus 9 is equal to 6 and we know that 6 is divisible by 3. So that means two numbers 15 and 9 are divisible by 3 then their difference 6 is also divisible by 3. Thus in this session we have learnt common factors, coplying numbers, common multiples and divisibility rules. With this we have finished this session. Hope you must have understood all the concepts. Goodbye, take care and have a nice day.