Prime Factorization of 18 | Math with Mr. J

Welcome to Math with Mr. J. In this video, I'm going to cover the prime factorization of 18. Remember, when it comes to prime factorization, we break a number down into its prime factors. These are 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 18, we need to start with two factors. Two numbers that multiply to give us 18. And we're going to start with those in order to break this number down. Well, 3 and 6 are factors of 18. 3 times 6 equals 18. So let's break this down into 3 and 6. Now you may be thinking 2 and 9 are factors of 18 as well. 2 times 9 equals 18. So would 2 and 9 work? Absolutely, that works too. Depending on the number, there may be different paths we can take. But in the end, we will get to the same prime numbers. And that's what's important. So there can be multiple ways to do these depending on the number. So keep that in mind. Now let's take a look at 3 and 6 and see if we can break this down any further. 3 is prime. So we are done over here. And I'm going to circle 3 to show that we have a prime number. 3 can't be broken down any further. 6, on the other hand, is a composite number. So we can continue to break that down. We need to think of factors. Well, 2 and 3 are factors of 6. 2 times 3 equals 6. So let's break this down into 2 and 3. 2 is prime and 3 is prime. So we are done. That's the prime factorization of 18. We can't break anything down any further. We have all prime numbers. So let's write this out as 18 equals. And then I'm going to put our prime numbers in order from least to greatest. And we're going to multiply. So we have 2 times 3 times 3. And if we have the correct prime numbers, they will multiply to equal our original number. 2 times 3 is 6. Times 3 is 18. So we are correct here. So there you have it. There's the prime factorization of 18. I hope that helped. Thanks so much for watching. Until next time, peace.