Prime Factorization of 48 | Math with Mr. J

Welcome to Math with Mr. J. In this video, I'm going to cover the prime factorization of 48. Remember, for the prime factorization of a number, we 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 48, we need to start breaking this down by thinking of two factors, two numbers that will multiply to give us 48. Well, 6 and 8 are factors of 48. 6 times 8 equals 48. So let's break 48 down into 6 and 8. Now there are other factors that we could have started with here. For example, we could have started with 2 and 24 as well, along with other options. These will all work out. Depending on the number, there can be multiple different factors that we can use. So there can be multiple ways to do these. But in the end, we will get the same prime numbers. And that's what's important. So keep that in mind. Now let's continue breaking this down. So we have 6 and 8. Both are composite numbers, so they both can be broken down further. Let's start with 6. Let's think of two factors here. Well, 2 and 3 are factors of 6. 2 times 3 equals 6. So let's break 6 down into 2 and 3. Now 2 and 3 are both prime numbers. We can't break those down any further. So let's circle those to show that we have prime numbers. Now let's go over to 8. So we need factors of 8 here. Well, 2 and 4 are factors of 8. 2 times 4 equals 8. So let's break this down to 2 and 4. 2 is a prime number, so we are done here. We can't break that down any further. So let's circle it. As far as 4, we can break 4 down. 4 is a composite number. So as far as factors of 4, 2 times 2 is 4. 2 is a factor of 4. So let's break this down to 2 and 2. 2 is prime, so we are done here and here. And that's the prime factorization of 48. We cannot break anything else down any further. We have all prime numbers. So let's write this out as 48 equals. And I'll write our prime numbers here in order from least to greatest. And we are multiplying them. So we have four 2s. So 2 times 2 times 2 times 2. And then one 3. So times 3. And if we have the correct prime numbers, we can multiply them. And they will equal the original number. So let's check here. 2 times 2 is 4. Times 2 is 8. Times 2 is 16. Times 3 is 48. So we are correct here. So there you have it. There's the prime factorization of 48. I hope that helped. Thanks so much for watching. Until next time. Peace.