Prime Factorisation: Factor Tree of Bases 2 and 3


It says factorize 72 as a product of these prime factors. Okay! So I want to write 72 as a product of its prime factors, so I have to find what the prime factors of 72 is, isn’t it? So how do we do that? Well, I’m going to use a little trick called the tree method.

Now, this method is really really helpful if you’re a bit confused about the stuff. I always use it as well, so I want you to kind of use this whenever you’re asked this kind of question, okay? So I’ll show you how I’m going to do that starting with something like this. So I put my 72 on the very top and I simply draw two branches like that. And I put a 2 here because 2, 72 is divisible by 2, isn’t it? Now you don’t have to do 2. You can do 3 as long as it’s a prime number but I always used like to start off with an easy small number, so I just chose 2 because it’s nice and simple. I know it’s this is even number, so it will go into 2.

So trying to get your prime factors down your left-hand side, okay? So you don’t get mixed up on either side, so keep your prime numbers always on the left branch. So what’s 72 divided by 2 guys? Should be 36. 36, I can break it down further. So I’m going to go and draw two branches again and again I’m going to divide by two. Now as I said guys, you don’t have to do 2, you can do 3 because I know that 36 is divisible by 3 as well. But again I just chose 2 for some reason, okay? You can do 3, it doesn’t really matter. So 36 divided by 2, it’s 18.

Now again I can break it down further. Draw two branches, I’m going to divide it by 2 again and then you should get 9. Now, 9, this time, I’m going to draw true branches two branches with 3 because I know that 3 goes into 9. So 9 divided by 3 is 3. We can’t actually break down 3 any further, right? Because 3 is a prime number. So I can’t break it down any further. As you can see as I kept the prime numbers down my left-hand side you can see all the prime factors over here, okay?

So now I only want you to concentrate on the left-hand side numbers including these 3. Don’t worry about 9, 18, and 36. Just the left-hand side numbers. I can say that 72 is 2 cubed and 3 squared. We multiply those together. So 72 is basically, I’ll just write over here. 2 times 2 times 2 times 3 times 3. You can check-in your calculator, you can put all that in you should get 72. That’s how I broke it down into the prime factors. But see how the 2 is here, there’s three lots of 2. So I simply simplify it as 2 to the power of 3 or 2 cubed and we multiply we keep the multiplication sign because it says we want it as a product and there’s two lots of 3. So it’s going to be 3 squared or 3 to the power of 2.

Okay, we’ve got a slightly bigger number but that doesn’t matter as long as we keep the same structure. So I’m going to start off with 108 and I’m going to divide it by 2 again which is going to get me 54. Now 54, I’m going to divide it by 2 again and I’m going to get 27 but 27, I can go divide it by 3. It should be 9. And 9, I can divide it by 3. It’s going to be 3. You stop when you can’t divide any further. 3 is a prime number. I can’t go any further.

So see how again I left the prime factors down my left. 108 is basically 2 times 2 times 3 times 3 times 3 but remember, I like to use some of my indices. So 108 is seen how there’s two lots of 2, so 2 squared and there’s three lots of 3, so 3 cubed and make sure you use the multiplication sign just to show that we’re multiplying them, okay?


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