TenMarks teaches you how to find prime factors of a number using tree method.
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Learn about Prime Factorization using Tree Method Let’s learn how to do prime factorization of a number using the tree method, and we are given three numbers, 4, 20 and 54 and we have to find the prime factorization of each using the tree method. So let’s do the first one. This is actually fun to do. In order to write the prime factors or determine the prime factors of a number, here’s what we’ll do. Step 1, we write the number. Step 2, we draw two arrows next to it, or write below it and we breakdown this number 4 into two values, one of which is a prime number. So 4, can only be broken down into 2 and 2, because 2 is the smallest prime number, so one is 2, and the other one is 2. Now what I do is I take the first prime number, keep it as it is. And the second one, we breakdown into prime numbers, if it is not already a prime number. In this case, 2 is a prime number, so the factors of this – the prime factors are 2 x 2 or 2², right? Prime factors of 4 are 2 x 2 or 2². So that’s how we do it. Now let’s try the second one. Let’s change the color of the pen so there’s no confusion and let’s try and find the factor of – prime factorization of 20. I'm going to create a little bit of space. So 20, I can break down into 2 numbers, 2 and 10. 2 is already a prime, so I can circle it. 10, I can break down further into 2 and 5. 2 is a prime number and 5 is a prime number as well, so I have my answer because I can’t break this down anymore. So the prime factorization of 20 is 2 x 2 x 5 or 2² x 5. Okay, this is the answer. You see how I did this? Now, let’s change the color again and do the third one which is 54. So let’s create a little bit more space and look at the number, 54. Well, how would I divide 54 into two? I would get 2 and 27. 2 is a prime number, 27 I can divide as 3 x 9. 3 is a prime number. Let’s take a little bit more space. 9 can still be divided into 3 and 3, both of which are prime numbers. So now that I can’t divide anymore, the prime factors are 2 x 3 x 3 x 3, right? 2 x 3 x 3 x 3 or 2 x 3³. So real quick to recap what we’ve learned, in order to do the prime factorization of a number, using a tree method, I place the number and we draw a tree, two different branches and we divide them into two units, one of which is a prime number. If the other one is a prime number, we’re done. In which case, 2 x 2 or 2², or 2 to the power of 2 is the answer. If we look at the bigger number like 20, we break it down into two, 2 and 10, one of which is prime. The other one, 10 is not prime so we break it down further into prime numbers, 2 and 5 which means this, this and this gives us the answer, 2 x 2 x 5 or 2² x 5. Same thing with the third one, 54, broken down into 2 x 27, 27 to 3 and 9, 9 into 3 and 3. We keep doing this until all the numbers are prime, okay? And then I simply multiply them or write them down in exponential fashion which is 2 x 3³.

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