Prime and Composite Numbers

Hello, and welcome to this video about prime and composite numbers! Today we’ll learn what prime and composite numbers are, how to classify numbers as prime or composite, and why this is important.

Before we get started, let’s review a few things. First, factors are numbers that you multiply together to get another number. For example, in the equation \(2\times{3}=6\), 2 and 3 are factors of 6. \(1\times{6}\) also equals 6, so 1 and 6 are factors as well. The answer to a multiplication problem is called the product. In the examples given, 6 is the product of \(2\times{3}\) and \(1\times{6}\).

A prime number is a number greater than 1 that is not the product of two smaller numbers. The only factors of a prime number are 1 and the number itself. For instance, 13 is a prime number because the only factors of 13 are 1 and 13. In other words, the only way to make a product of 13 is by multiplying \(1\times{13}\).

In contrast, a composite number is a positive number that is the product of two smaller numbers. A composite number can have many factors. For example, 12 is a composite number because it has several factors: \(1\times{12}\), \(2\times{6}\), and \(3\times{4}\). Since there are many ways to multiply to get a product of 12, it is classified as a composite number.

All positive integers are either prime or composite. To determine whether a number is prime or composite, simply list all the factors of that number. In other words, list all the ways that you can multiply to get the number in question as the product. If the number has many factors, then it is composite. If the only factors are 1 and the number itself, then it’s prime.

Let’s take a look at an example together. Determine whether 24 is a prime or composite number. To do so, make a list of all the factors of 24. Remember, factors are numbers that are multiplied together to get a product. In this case, the product is 24.

Start with 1 and work your way up from there. Ask yourself, “1 times what number equals 24?” \(1\times {24}=24\), so 1 and 24 are factors. Next is 2. 2 times what number equals 24? \(2\times{12}=24\), so 2 and 12 are also factors of 24. After 2 is 3. 3 times what number equals 24? \(3\times{8}=24\), so 3 and 8 are factors of 24 as well. After 3 comes 4. 4 times what number equals 24? \(4\times{6}=24\), so 4 and 6 are factors of 24.

Now let’s move on to 5. 5 times what number equals 24? Since there isn’t a number we can multiply by 5 to get a product of 24, 5 is not a factor. Therefore, we can skip 5 and move on to 6. 6 times what equals 24? Well, \(6\times{4}=24\), so 6 and 4 are factors of 24. But notice that we’ve already named these numbers as factors of 24, since \(4\times{6}=24\). Repeating factors indicate there are no more factors of 24, we’ve already named them all.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Since there are several factors of 24, this is a composite number.

Let’s take a look at another example together. Determine whether 11 is prime or composite. To do so, make a list of all the factors of 11. Remember, these are all the numbers we can multiply to get a product of 11.

Let’s start with 1. Ask yourself, “1 times what number equals 11?” \(1\times{11}=11\), so 1 and 11 are factors. Next is 2. Nothing times 2 is 11, so we can skip 2 and move onto 3. You can’t multiply anything by 3 to get 11, so move onto 4. Again, nothing times 4 equals 11, so 4 is not a factor. Let’s move onto 5. 5 times what number equals 11? Since there isn’t a number we can multiply by 5 to get to 11, 5 is not a factor either. What about 6? Well, \(6\times{1}=6\), and \(6\times{2}=12\). So there aren’t any numbers we can multiply by 6 to get to 11.

7, 8, 9, and 10 aren’t factors of 11 either. 11 is a factor because \(1\times{11}=11\). However, we’ve already listed 1 and 11 as factors. Since these are the only two factors of 11, that means it’s a prime number because the only way to get a product of 11 is by multiplying it by 1 and 11.

Now it’s your turn. List the factors of 18 to determine whether it’s prime or composite. Pause the video here and try this one yourself. When you’re done, resume the video and we’ll go over it together.

To determine whether 18 is a prime or composite number, make a list of all the factors of 18. Remember, these are all the numbers we can multiply to get a product of 18.

Start with 1. Ask yourself, “1 times what number equals 18?” \(1\times{18}=18\), so 1 and 18 are factors. Next is 2. \(2\times{9}=18\), so 2 and 9 are factors. What about 3? Well, \(3\times{6}=18\), so 3 and 6 are factors.

Next comes 4. 4 times what number equals 18? Since there isn’t a number we can multiply by 4 to get to 18, 4 is not a factor. Skip it and move onto the next number, which is 5. Nothing time 5 is 18, so 5 is also not a factor. Skip it and move onto the next number, which is 6. \(6\times{3}=18\), so 6 and 3 are factors. But we’ve already named these numbers as factors of 18, because \(3\times{6}=18\). Repeating factors indicate that there are no more factors of 18, and we have already named them all.

So the factors of 18 are 1, 2, 3, 6, 9, and 18. Since there are several factors of 18, we can classify it as a composite number.

Great job!

Many patterns and number concepts rely on prime numbers, as well as expressing composite numbers as the product of their prime numbers. For instance, computer encryption relies on prime numbers and prime factorization. Factoring large numbers can take a really long time, even for computers. As a result, prime numbers and factorization are used for encryption purposes to protect confidential data. Some examples involving encryption include logging into your bank account’s website, inputting your credit card information to make an online purchase, and sending a confidential email.

Let’s take a look at one more example together.

The area of a rectangular patio is 39 square feet. What are the possible whole number dimensions of the patio?

To find the area of a rectangle, multiply length times width. In this case, we know that the area is 39 square feet. What numbers can we multiply together to get a product of 39? To answer this question, make a list of all the factors of 39.

Let’s start with 1. Ask yourself, “1 times what number equals 39?” \(1\times{39}=39\), so 1 and 39 are factors. Next comes 2. 2 times what equals 39? Well, there isn’t a number we can multiply by 2 to get to 39, so 2 is not a factor. We skip it and move onto the next number, which is 3. \(3\times{13}=39\), so 3 and 13 are factors. Working our way through the next several numbers, there are no other factors of 39.

Therefore, the possible dimensions of a patio with an area of 39 square feet are: 1 foot by 39 feet and 3 feet by 13 feet.

Since there are several factors of 39, we can classify it as a composite number.

Review

I have one more problem for you to try. This one’s a little more difficult, but I know you can handle it. Take a look at the problem, pause the video, and try it yourself. When you’re done, resume the video and we’ll go over everything together.

The area of a rectangular shed is 84 square feet. List all possible whole number dimensions of the shed. Is the area of the shed a prime or composite number? How do you know?

Pause the video here and see if you can answer these questions yourself.

To find the area of our rectangle, multiply the length times the width. In this case, we know that the area is 84 square feet. So what numbers can we multiply together to get a product of 84? To answer this question, we just have to make a list of all the factors of 84.

Here are the factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.

Therefore, the possible dimensions of a garden with an area of 84 square feet are: 1 foot by 84 feet, 2 feet by 42 feet, 3 feet by 28 feet, 4 feet by 21 feet, 6 feet by 14 feet, and 7 feet by 12 feet.

Since there are several factors of 84, we can classify it as a composite number.

Nice work!

I hope this video about prime and composite numbers was helpful. Thanks for watching, and happy studying!

Prime and Composite Number Practice Questions