The Euclidean Algorithm (GCD or GCF)

(male) Hey there, it’s Mr. Marcos and we are going to learn about the Euclidean Algorithm. Euclid was a man that you may or may not have heard of. We’ll learn about him later maybe in a video and an algorithm is a process or a way of doing things over and over again. And this is a process to find
the GCD of some numbers… the greatest common divisor or
also known as the greatest common factor. and again for a different video we can go more into depth about what, what that means. But for now, if you know you wanna find the GCD of some numbers you can use the Euclidean Algorithm. So what you do is you take the large number and you put it inside the dividend and you divide them. So 12 goes into 30 and you go 2.
So it’s 24 and you get 6 remaining. Now what you do is you take the remainder and divide it into the divisor. So we take the 12 down here. 6 goes into 12 two times. And you get 12, zero remainder. And when you get zero, you stop and the final divisor is your answer. So there is our GCD of 12 and 30. Pretty simple. Let’s do another one. GCD of 216 and 594. OK So we take 594 and we divide it by 216. And it goes in… let’s see… 216 twice is 432. So it looks like it’s gonna go 2 times. 432… you get 2, 6, 1 left over. Now you take the 216 and you divide that by the 162 remainder. And it’s going to go one time. You get 54. I need a lttle bit of room so I’m gonna just get this whole thing shifted a little bit. OK, now I’m going to divide 54 into 162,
which is the divisor. 54 goes in… exactly three times. We got to zero. Therefore our answer is 54.
So the GCD of 216 and 594 is 54. Pretty simple. Pretty cool.
Thank you.

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