 If someone asked me to find the hcf of 387 and 201, I would say I can do it but from what we know so far it's going to be a very lengthy and tedious process, I am not going to enjoy doing it at all, I don't enjoy division, dividing these by so many numbers and then finding their prime factors or using Euclid's division lemma, both of them are going to be very tedious for two big numbers. In this video I am going to show you a method or a property of hcf that will help you to solve these kind of problems and many other kind of problems fairly easily, without much division at all. You're going to enjoy this one. Let me write down this property for you, hcf of two numbers a comma b is the same as the hcf of a comma b plus a into k where k is any integer. At first glance this might seem like a normal property that you read in the books but this is such a powerful property as we're going to see now. What it is saying is if you have two numbers a and b keep one of the numbers as it is for the second number you can add any multiple of the first number and because k is an integer and integers have negative numbers you can even subtract any multiple of the first number. So keep one of the numbers the same and add or subtract any multiple of that number into the second number. Okay let's let's try to use this. So 387 and 201. Here a and b are positive numbers so I want to keep both of them positive. So let me subtract 201 from 387. Let's see what I'll get 387 minus 201. This will give me 6, 8 and 1. So this should be equal to hcf of 186 and 201. So I kept one number as the same and I subtracted one multiple of 201 from 387. I get 186 and 201. I can do this again. Now I can keep 186 as the same and subtract this from 201. So I'm keeping 186 as the same and I'm subtracting 186 from 201. So I can't subtract 2 times 186 because then it will become negative. So I'm just subtracting the first multiple. Let's see what I get. So this gives me 1 and then 9 and then 11 minus 6 15 11 minus 6 5 and 19 minus 18 is 1. So this is 15. So 186 and 15. Okay, now we have a pretty small number. Now see, now we can subtract one multiple of 15. We can keep 15 as the same and subtract one multiple of 15 from 186. But since 186 is so much larger than 15, we can subtract 15 into maybe 10. That is 150. We can even subtract 15 into 11. That's 165. What about 15 into 12? That is 165. That is 180. 15 into 12 is 180. So I want to subtract 15 into 12 from 186. So 186 minus 180. That will give me just 6. So hcf of 6 and 15 is the same as hcf of 387 and 201. Are you kidding me? These huge numbers have been reduced to such small numbers. Okay, this seems pretty easy. But I just want to exploit this rule even more and make it even more simpler for me. I don't want to think at all. So let me keep 6 as the same and subtract 6 from 15. That gives me 9. Okay, I can easily find this hcf but I want to still go on abusing this rule. Again, I want to keep 6 the same and subtract from 9. So this would give me 3. In fact, I could have just subtracted 12 from 15 because that is a multiple of 6. But okay, I'm getting excited here. And finally, I can keep 3 the same and subtract that from 6. So I get hcf of 3 and 3. This is 3. This is the common factor between 3 and 3. So the answer of this problem is 3 and we found it using this property. In the next video, we will see the proof of this property and some other corollaries that we can prove using it. And all of these are also going to be very important in solving problems. But I was just so happy to have found this property. Now I hope hcfs don't look as scary as they were before.