Prime Factorization of 36 | Math with Mr. J

[Music] Welcome to Math with Mr. J. In this video, I'm going to cover the prime factorization of 36. Remember, for the prime factorization of a number, we can break the number down into its prime factors. The prime numbers that multiply to equal the original number. So, we are decomposing a number, breaking a number down to only prime numbers. So looking at 36, we need to start breaking this down by thinking of two factors. Two numbers that will multiply to give us 36. Well, 6 * 6 = 36. 6 is a factor of 36. So let's break 36 down into 6 and 6. Now keep in mind depending on the number there can be multiple different factors that we can use. For example, we could have started with 3 and 12 for this along with some other options and those would all work. There may be different paths we can take for these but in the end we will get the same prime numbers and that's what's important. So there can be multiple ways to do these. Now let's continue breaking this down. So we have six and six. We need to go from here until we only have prime numbers. Six is a composite number. So we can break these sixes down further. So we need to think of two factors. Well 2 and 3 are factors of 6. 2 * 3 = 6. So let's break these sixes down into two and three. Now two and three are both prime numbers. So we are done. We can't break any of this down any further. So let's circle these prime numbers to show that we have prime numbers and that we can't break them down any further. That's the prime factorization of 36. So let's write this out as 36 equals and then we can write out our prime factors in order from least to greatest and we are multiplying them. So we have 2 * 2 * 3 * 3 and if we have the correct prime numbers they will multiply to equal our original number. Let's check. 2 * 2 is 4 * 3 is 12 * 3 is 36. So, we are correct here. So, there you have it. There's the prime factorization of 36. I hope that helped. Thanks so much for watching. Until next time, peace.