TenMarks teaches you how to find the greatest common factor of numbers by using prime factors.
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How to Find Greatest Common Factor by Using Prime Factors In this track, we will learn about how do we get GCF or compute the Greatest Common Factor using the prime factor method. We’ve got two interesting questions. The first question says, “find the Greatest Common Factor of 18 and 45 by using the prime factor method.” Let’s do that first. So the numbers that are given to us are 18 and 45. So in order to use the prime factor method, the first thing I do is to look at step 1, which is compute, the prime factors of the numbers. Get the prime factors of the numbers. What are prime factors? Let’s take 18. 18 = 1 x 18. Now, I can make this the same as 18, I can breakdown and say that this is the same as 1 x 2 x 9. Now I can breakdown 9 even further which is 1 x 2 x 3 x 3, right? Out of these, this is a prime number, this is a prime number, this is a prime number, right? A prime number is a number that can be divisible by 1 or itself. Now, let’s look at the second number which is 45, 45 I can write as 1 x 45. I can breakdown further 45 as 1 x 3 x 15, which is the same as 1 x 3 x 3 x 5. Now all of these are either 1 or prime numbers, 3, 3, and 5 are all prime numbers which means I can’t break it down anymore. So the second step that I do is I find the common prime numbers or the prime factors. What is common? The common prime factors are, in this case, the common are 3 and 3 and 3 and 3, that’s what’s common. So the common prime factors are 3 and 3, right? And to compute the GCF, step 3 is multiply the common prime factors to get the GCF. All I have to do is multiply 3 x 3 which gives me 9, that is the GCF, okay? Now, once we’ve done that, let’s make sure we had to compute the Greatest Common Factor of 18 and 45, and that answer is 9, okay? Let’s look at the second question, I will change the color of my pen. The second question says, “Find the greatest number that will divide 445, 572 and 699 leaving the remainders 4, 5 and 6 respectively.” I'm going to go onto some empty space and let’s write down the numbers. The numbers are 445, 572, and 699. I know that I need to find the number which will divide each one of these and leave the remainder 4, 5 and 6 respectively. Okay? This is the remainder that should be left. If we know that this is the remainder that should be left, what we do is we subtract the remainder first. So I subtract this, to get 441, from this I get 567, and here I guess is 693. Because I know the remainder is going to be left anyway, let’s take that out and find the number which will divide all three. All of these three, each one of these three should be divided by the same number in perfect harmony. So in order to do that, let’s compute the GCF off – that number is the GCF, GCF of 441, 567, and 693. Let’s use the prime factor method. So what do I know about 441? 441 is 3 x 147, which is the same as 3 x 3 x 49, which is the same as 3 x 3 x 7 x 7, okay? All of these are prime numbers, so I can stop. Similarly, 567 can be written as 3 x 189, which can be written as 3 x 3 x 63, which can be written as 3 x 3 x 3 x 21, which is the same as 3 x 3 x 3 x 3 x 7. All of these are prime numbers. Okay, now let’s look at the third number which is 693. 693 is the same as 3 x 231, which is the same as 3 x 3 x 77, which is the same as 3 x 3 x 7 x 11. Okay? So these are the prime factors for each one of these. Step two, I have to compute the common prime factors. Well, 3 appears twice here, twice here, and twice here. So the common factors are – the common prime factors between all three are, I know it is 3 x 3, I got that. So, this is common. 7 is common in all three and the second 7 doesn’t exist here and 1 doesn’t exist. So the common prime factors are 3, 3 and 7. And if I multiply then, I get 9 x 7 which is 63, which is the Greatest Common Factor or GCF. Okay, 63. So let’s quickly recap what we learned. In order to compute GCF by the prime factor method, right? By the prime factor method, I write down both the numbers, writi