Prime Factorisation: Factor Tree of Bases 5 and 7

Prime Factorisation Factor Tree of Bases 5 and 7


So 625, now because it ends in 5. I’m sure that it’s going to be divisible by 5, so I started off by using my prime factor of 5. So I’m going to divide by 5. So you can go and do the division by yourself, it should be 1225 and this ends in 5 again. So I’m just going to divide it by 5 because I’m sure that’s going to be divisible by 5. So that divided by 5 is 245. So you can see the numbers getting smaller and smaller which is good. And I’m going to divide it by 5 again which is 49 and you can see 49 if I divide it by 7.

It’s going to be 7, yeah. 49 divided by 7 is 7. And 7 is a prime number. So I can’t divide any further, so that’s when I stop. Although the number we started off with is pretty big the tree diagram is not that big after all and you can see that 6125 is 5 times 5 times 5 times 7 times 7. Again you don’t have to worry about these numbers. Only the outside numbers on the left, okay? And again you can see there’s three 5, three lots of 5 and two 7, two lots of 7. So if I write it as my indices and product, it’s going to be 5 cubed times 7 squared.

So 300 now! It’s pretty small, so you guys can try it by yourself if you like. So 300, I’m gonna divide it by 2. So it’s going to be 150, of course, I’m gonna divide it by 5 because it ends in 0 and if I can I know it divides by 5 because if I divide by 5, it’s going to be 30. So it’s going getting smaller and smaller. Now 30. What should I do? I’m going to divide by 5 again and again. Guys, you can do it with 2 if you like eventually, we get the same answer, same lots of the prime factors, so you don’t have to worry about which one to choose. Just as long as it divides into it, that’s what you need to do. All right?

So you don’t have to do 5, you can do 2 if you like because 30 goes into 2 as well. But anyway I’m going to stick with 5. 30 divided by 5 is 6 and 6 if I divide it by 2, I’m going to get 3. Okay? And again you can’t go any further than that Concentrating on these numbers on your left, we know that 300 is 2 times 5 times 5 times 2 times 3, okay? Now see how for 2, this although it’s not together I can see there’s two 2’s, so there’s two lots of 2, there’s two lots of 5 and just one 3. So this time how would you write it?

I’m gonna write it as 2 squared because there’s two lots of 2, 5 squared because there’s two lots of 5, and 3 is just by itself. So it’s 3 to the power of 1
which is just 3, okay? So that’s pretty much it. Just remember guys 3 to the power of 1 is just 3, you don’t have to write the 1 there, okay? So yeah just remember that.

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