What are Prime Numbers Math with Mr J

Welcome to Math with Mr. In this video, I'm going to cover what prime numbers are. Now, prime numbers are whole numbers with only two factors, one and the number itself. So, we're going to go through few examples of prime numbers to better understand that, and then take look at five other numbers and determine if they are prime or not prime. So, let's jump into our first example of three. Now, three is whole number, so we need to take look at its factors to see if it only has two. Factors are the numbers that we multiply together to get another number. Now, you can think of factors as the numbers that can go into three. That's not the most mathematical or technical definition of factors, but it can help as we're thinking of the factors of any number. So, the only numbers that can go into three, the only factors of three are one and three. 1 * 3 = 3. For example, we can't use two because 2 * 1 is 2, 2 * 2 is 4, 2 * 3 is 6, so on and so forth. It doesn't equal three at any point. So, the only factors are one and three, one and the number three itself. So, three is prime. And this is the same case for example two and example three. So, think of the factors of seven. What numbers can we multiply together to equal seven or what numbers go into seven? Only one and seven. One and the number seven itself. 1 * 7 or 7 * 1 = 7. Same for 19. 19, the only factors are one and 19. One and the number itself. So, let's take look at five other examples and see if they are prime or not prime. So, let's take look at number one on the right-hand side of the screen where we have two. Now, two is very unique number and we'll see why here in second. So, let's think of the factors of two, the numbers that go into two. Well, it's only one and two. So, one and the number itself, two. So, two is prime number and it's unique because it's the only even number that's prime. Any other even number is automatically not prime. So, let's take look at number two where we have 21. So, let's think of the factors or multiplication facts that equal 21 or the numbers that go into 21. However, it works best as far as you're thinking and coming up with factors. So, we know that one * 21 = 21. So, one and 21 are factors, but also three and seven. And I'll add 21 to the end there. So, 21 has more than two factors, more than one and itself. So, 21 is not prime. It's considered composite number. And actually have video about composite numbers where go into more detail. I'll drop that down in the description. On to number three where we have 13. So, the only factors of 13 are one and 13. So, one and the number 13 itself. So, 13 is prime. Next, we have eight. So, we know one and eight are factors, but also two and four can go into eight. 2 * 4 = 8. So, two and four are factors. So, we have more than two factors there. So, eight is composite. It is not prime. And lastly, number five, we have 5,462. Now, we do not want to write out all of the factors for that number to determine if it's prime or not. We can automatically tell because like we mentioned earlier, all even numbers except two are composite. They are not prime because we know two is factor of all even numbers. So, we know for sure that one, two, 5,462 as well. So, these are three factors right off the bat plus more. So, if we have more than two, number is automatically composite, therefore not prime. So, this one is not prime because it's even and we can tell that without listing out all the factors. So, there you have it. There's the basics of prime numbers. hope that helped. Thanks so much for watching. Until next time, peace.