 In this video, let's talk about the greatest common divisor for a fraction. So for this, let us revisit the term divisor. When we talked about integers, so this is us talking about integers, we said the divisor of an integer, let's say 10 is such a number, which when 10 is divided by, we get another integer. For example, 2 is a divisor of 10, because when 10 divides by 2, we get 5. Similarly, 1 is a divisor of 10, because when 10 divides by 1, we get 10. So similarly, we can find other divisors of integers. What about fractions now? How can we define divisors of fraction? Now the problem here is that if we divide any fraction, let's say 3 by 4 with any other fraction, let's say 15 by 27, we know that what we will get is also going to be a fraction. So if all of these are fractions, there is nothing special about these divisors. So we need to define our divisors in a special way. So to make our divisors a little bit more special, we say that the divisor of a fraction, let's say we are finding the divisor of 3 by 4, will be such a number, which when 3 by 4 is divided by, we should get an integer, not a fraction, but an integer. So this has to be such a number, which divides our original number in such a way that we get an integer. That is now our divisor. So we now understand what is the divisor for a fraction. Let's see some examples. 1 by 4, what is a divisor of 1 by 4? Let's see. Is 1 by 2 a divisor of 1 by 4? Let's see, 1 by 4 divided by 1 by 2, this will give me 2 by 4, which is half. This is not an integer. So therefore, 1 by 2 is not a divisor. What about 1 by 8? Is this a divisor? If we divide this, we get 8 by 4, which is equal to 2. This is an integer. So therefore, this is a divisor. And this makes sense, right? If we talk about a circle, we divide it into 4 halves. This is 1 fourth, 1 eighth divides our 1 fourth into 2 integral halves, into 2 integers. So therefore, this is a divisor, 1 by 8 is a divisor of 1 by 4. So now we know how to find a divisor for a fraction. We just want to find a number which divides our original number evenly. Just like we used to before, 2 divides 10 evenly into 5 halves. Similarly, 1 by 2, no, not 1 by 2, 1 by 8 divides 1 by 4 evenly into 2 halves. Now based on this, let's talk about the greatest common divisors of 2 fractions. For this video, let's take a simple example, GCD of half and 1 by 4. Before I tell you, how about you pause this video and give it a shot yourself? I hope you have tried this. How about we do this the old way? Let's list down the divisors for 1 by 4 and 1 by 2 and find the one that is common and the greatest. So for 1 by 4, we know that 1 by 4 is one of the divisors for 1 by 4. Because if we divide 1 by 4 by 1 by 4, we get 1 which is an integer. What about 1 by 8? Yes, we just saw that 1 by 8 also divides 1 by 4 evenly. So therefore this is also a divisor. Similarly 1 by 12, 1 by 16, these are all divisors of 1 by 4. And we can see that these go on decreasing. We can say that 1 by 4 here is the greatest divisor of 1 by 4. We cannot have a number more than 1 by 4 which divides 1 by 4 evenly. Just like integers, in integers as well, the greatest integer that can divide 5 evenly is 5. The greatest integer that can divide 10 evenly is 10. A number greater than 10 will not be able to divide 10 evenly. So 1 by 4 is the greatest divisor of 1 by 4. Similarly if we list down the divisor of 1 by 2, we get 1 by 2, 1 by 4, 1 by 6 and so on. Now we can clearly see the greatest common divisor, 1 by 4. 1 by 8 here will be another common divisor but it is not the greatest, 1 by 4 is the greatest. Therefore this will have an answer of 1 by 4. So in this video we did this the brute way, the basic way. We understood what divisors of fractions are and we found out the greatest common divisor for a pretty simple pair. In the next video, we learned a trick to find the greatest common divisors of fractions which are not so friendly.