Prime Factorization: Birthday cake method and Factor Tree Method

welcome to moomoomath and science in this video I'd like to talk about two different ways for prime factorization prime factorization is the process of finding which prime numbers multiply together to make the original number in this video I'd like to first go over prime factorization using a factor tree and then the second way is using what is called the cake method so let's get started first with a factor tree and I will first find the prime factorization of 78 using a factor tree first thing I do is I write out 78 78 can be divided by 2 and 2 goes into 78 39 times so I will draw them underneath 78 I will circle 2 because it is prime and 2 times 39 is 78 next I know that 3 will go into 39 so 3 times 13 is 39 I will circle both of these because they are prime so at this point I have all prime numbers so the prime factorization of 78 is 2 times 3 times 13 next example with the factor tree is 85 I know 5 will go into 85 5 times 17 is 85 I will circle both of these because they are prime so the prime factorization of 85 is 5 times 17 now the cake method is a little bit different I'll start with a very basic one you first write out the number that you need to find the prime factorization for which is 18 I will put brackets over it so that it begins to look like a cake I know 2 will go into 18 nine times so I will write the nine above the 18 and draw another bracket next 3 goes into 9 three times so I will write three above the 9 draw another bracket and then I know that the only prime number that will go into 3 is 3 I'll write this on the outside and put a 1 on the top and it looks like so therefore the prime factorization of 18 is 2 times 3 times 3 let's work another example 72 I will write a bracket over 72 2 goes into 72 so I'll write 36 above the 72 and draw another bracket next 2 will go into 36 18 times next 3 excuse me - will go into 18 nine times so I'll write the night and then three will go into 9 three times and 3 is divisible by three I put a 1 on the top looks like your candle so now I have the prime factorization of 72 is 2 times 2 times 2 times 3 times 3 so there we go two methods for prime factorization choose which one you like best thanks for watching and moomoomath uploads a new math and science video every day please subscribe and share