Math Tutorial: Prime and Composite Numbers

Hello. This is Mr. Vic. And today we're going to work on prime numbers. Are you ready? OK. Let's start by going over some key definitions and some examples. The first is a prime number. Now, a prime number is a number that has only two factors, 1 and itself. Again, a prime number is a number that has only two factors, one and itself. Remember that.

Notice the examples. 3. The factors of 3 are only 3 and 1. Notice 3 times 1 equals 3. So the factors are 3 and 1. Notice the factors of 7 are 1 and 7. 1 times 7 equals 7. These are the only two numbers that can be multiplied together that equal 7.

So, again, the factors are, 3 and 1 and 7 and 1. Notice they only have two numbers. Remember the definition of prime numbers. The number that has only two factors, 1 and itself. 1 and itself. 1 and itself. Remember that. Let's move on to composite number.

Now, composite number is a number that has three or more factors. So composite numbers have three or more factors. Prime number has only two factors, OK? So, again, a composite number is a number that has three or more factors. Now, notice the examples. 4 equals 4 times 1 or 2 times 2. So the factors are 1, 2 and 4. Now, 10, the factors are 1 times 10, 1 in 10, and 2 times 5, 2 and 5. So the factors, again, are 1, 2, 5, and 10.

Notice, remember the definition. A composite number has three or more factors. So notice we have one, two, three factors. And notice here we have one, two, three, four factors. Three or more. Composite numbers. Prime numbers. Let's move on, OK? Let's go down a little bit. Let's look at some more examples. Notice we have numbers 8, 8.

What we've done is, we've drawn some arrays. Notice we have 1 times 8 equals 8. And 4 times 2 equals 8. So the factors based upon this array are 1 and 2, 4 and 8. Notice it has four factors. So is this going to be a prime, or a composite number? What do you think? Prime or composite? Well, remember the definition. A composite numbers has three or more. So this is going to be definitely a composite number.

Let's look at the next example. Notice the number 11. Notice the array. The only way we can draw is 1 and 11. 1 times 11 is 11. Notice we only have two factors. So is this going to be prime or composite? Well, definitely it's going to be a prime number. Remember a prime number is a number that has only two factors. A composite number has three or more. Four factors here and two factors there. Composite, prime.

Let's move on, OK? Notice we have a prime number chart here. Notice it's 1 through 100. So these are the most common prime numbers. OK? Notice we have 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. Again, most common prime numbers. Very important to remember some of these. But also, remember, if you know your multiplication facts, it's easy a way for you to memorize this by memorizing all your multiplication facts.

OK. Let's keep going. I'm going to scroll down a little bit. Let's work on a couple of examples. Notice that as the directions say, is the following number prime or composite? Prime or composite? OK. Number 19. Well, I know that one factor has to be 1 times 19. Any other factors? Let's see. 2 times 7? No. 6 times 3? No. 10 times 2? No. 4 times 5? No. That's it. So we only have two factors, 1 and 19. That means that 19 is a prime number. Because, remember, a prime number has only two factors, 1 and itself.

Let's look at number two. We have 24. OK. Let's write some of the factors out. Well, I know that 1 times 24 is 24. So we got 1 and 24. Let's see here. How about 4 times 6? That works. So we know we have 4 and 6. How about 2 times 12? That works. 2 times 12. Let me erase that. 2 times 12. That works. 2 times 12 is 24, so that's 2 and 12. Anything else? Oh, yeah. What about 3 times 8? So we have 3 and 8 are factors. Notice all our factors. 1, 24, 4, 6, 2, 12, 3, and 8. 1, 2, 3, 4, 5, 6, 7, 8 factors. That means that 24 has to be a composite number. Remember a composite number has only had three or more factors. Remember a prime number has only two.

Let's look at 45. Well, 45-- new color-- 45, I know that one of the factors has to be 1 times itself, 1 in 45. Also, 9 times 5 is definitely a factor because it ends in 5, so it has to be a multiple of 5. So we have 1, 45, 9, and 5. 1, 2, 3, 4 factors. So, is this going to be a prime or composite? Well, this is going to be a composite number. Remember composite numbers have three or more factors. So definitely 45 is a composite number.

Let's look at 31. Well, I know one factor has to be 1 and itself, so 1 times 31. So I know the factors are definitely going to be 1 and 31. Anything else? How about a 6 and 5? That's 30. That doesn't work. 11 and 3? No. 9 and 3? No. 10 and 3? No. That's it. So we only have two factors, 1 and 31. So is that going to be a prime or composite? Well, that's going to be a prime number because, remember, prime numbers have only two factors, 1 and itself. So 31 is definitely a prime number. Well, I hope this helps you. Always try your best. Practice makes perfect. Work well.

Good job. Let's keep going. Scroll down a little bit. Next, we have solve. Write all the factors. Determine if their number is prime or composite, OK? So we're going to solve. Write all the factors. Determine if the number is prime or composite, OK? So, 8. Let's figure out all the factors of 8, OK? So let's write them out. Let's get a different color. Well, I know I can multiply 1 times 8, and that will equal 8. OK. What else? 2 times 4 equals 8. Can you think of anything else? 3 times 6? No. 3 times 2? No. 3 times 3? 5 times 4? No. No, that's it. So the factors are-- let's see here-- 1, 8, 2, and 4. Those all are factors.

Now we determine if it's prime or composite. Well, if you remember our rules, a prime number only has two factors. A composite number has more than two. So this is going to be a composite number. Remember that, OK?

Next, 17. Let's write the factors of 17. I know I can multiply it 1 and times itself. 1 times 17 equals 17, OK? So we've got one set, so far. How about 2 times 8? Well, 2 times 8 is 16. That doesn't work. OK. 3 times 6 is 18. That doesn't work. 4 times 4 is 16. Close. That doesn't work. 5 times 4, that's 20. It doesn't work. That's it. So our factors are 1 and 17. Do you remember our definitions? A prime number is a number that its only factors are 1 and itself. It has only two factors, 1 and itself. So 1 and itself. So this must be a prime number. Remember a composite has more than two. So this is a prime number.

I'm going to scroll down a little bit. Let's keep going. Next, it says, "Solve. Is each number prime or composite?" Wow. So let's try to figure this out. You need to remember your definition. Prime or composite, OK? So prime number, remember, only has two factors. A composite has more than two. OK? That's helpful, OK? Remember that. I'll circle it.

OK. 25. Let's write the factors of 25. 1 times 25. OK. That works. What else do we have? 10 times 2? No. 10 times 3? No. Oh, I forgot. 5 times 5. Anything else you can think of? 6 times 4? No, that's 24. That doesn't work. 7 times 3? 21. No, it doesn't work. So that's it. So our factors are 1, 25, and 5. No need to write 5 twice. 1, 25, and 5. So we have-- how many numbers we have? We have one, two, three factors. Three factors. More than two? So that must mean that this is a composite number. Remember, a prime number only has two, so this is a composite number.

Let's look at 31. Wow, 31. That's a big number. OK. Let's do 1 times 31. That's obvious, 1 times 31 equals 31. How about, 2 times 15? That 30. That doesn't work. 2 times 16? That's 32. That doesn't work. 4 times 6? No, it doesn't work. How about 5 times 6? Oh, that's 30. That doesn't work. 9 times 3? No, that's 27. That doesn't work. Well, that's it. So our factors are 1 and 31. Oh, 1 and itself. 1 and itself. That must mean it's a prime number. Good job.

Let's go down. Let's keep going. Our last number, number 5, is a problem that I want you to do. I want you to work with this number. I want you to determine if 100 is prime or composite. Click A or B. Once you're done, we are going to review our problem and move on, OK?

Good job. B is the correct answer. Do you know why? Let's go over it. Composite is the correct answer. Let's look at 100 here. The factors of 100 are, well, we know that 1 and itself, 1 times 100. OK? Well, 10 times 10 is 100. What else? 50 times 2 equals 100. Do you know any more? I do. How about 20 times 5? It's 100. Anything else? Are we missing any? Oh, yeah. We're missing one. 25 times 4 equals 100. Notice all the factors that we have. 1, 100, 10, 50, 2, 20, 5, and 25, and 4. All these are factors. One, two, three, four, five, six, seven, eight, nine. Nine different factors. And if you remember our definitions, a prime number only has two. A composite number has more than two. So the correct answer is B. Well, I hope this helps you. Practice makes perfect. Try your best. Work well.